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A special cosine is not periodic...

Asked by: Alfred_F 450
December 04 2024
1  5

Prove: If a is an irrational number, then the function y = cos (ax) + cos x is not periodic.
Is it possible to graphically represent or calculate this fact using an example?

Apply Bilinear form for some PDE...

Asked by: salim-barzani 1715
pde differential-equations incomplete-question
December 03 2024
0  1

I try to get some Bilinear form for some PDE equation  and already i have algorithm by writing in lecture but i can't apply i don't what is mistake i did, and i didn't seen some of this lecture code in maple  like (myint(expr,var))
 i  do upload PIcture of algorithm and example which they get Bilinear form 

Bilinear.mw

thanks for any help

Triangle Wanted in Red and Black - an old riddle...

Asked by: Alfred_F 450
recreational-mathematics
December 02 2024
1  18

If a point is chosen in the Euclidean plane, then it is red or black.
It must be proven that there is then an equilateral triangle with corners of the same color.

dsolve gets stuck...

Asked by: Scot Gould 1059
December 02 2024
1  4

dsolve gets stuck on a problem. Attached is the worksheet.

In Case I, dsolve solves the two ODEs separately. In Case II, dsolve solves them together, but only if I define a constant. In Case III the constant is not defined. dsolve never returns, and I have to hit the stop sign. The question I have: Is there a consistent method to the failure so that I can avoid the problem in the future with other ODEs?

dsolve_bug.mw

What "style" are the icons?...

Asked by: Scot Gould 1059
2dmath font style
December 01 2024
1  0

Question: Is there a style for the icons from the palettes? 

(The rest of this post is a screenshot because MaplePrimes can't show the change in fonts.)s a

DataFrame display alpha as a Greek letter...

Asked by: Ronan 1381
typesetting greek dataframe
December 01 2024
1  4

How do I get alpha to display as the Greek letter in DataFrame Row column?

> 

restart
> 

#varp:=alpha
> 

QQFProj := proc(q12::algebraic, q23::algebraic,
                q34::algebraic, q14::algebraic,{varp:=:-alpha},
                  prnt::boolean:=true) #{columns:=[QQFproj,Q13proj,Q24proj]}
  description "Projective quadruple quad formula and intermediate 13 and 24 quads. Useful for cyclic quadrilaterals";
  local qqf,q13,q24, sub1,sub2,sub3, R,values,DF,lens;
  uses   DocumentTools;
  sub1:= (q12 + q23 + q34 + q14);
  sub2:=-4*(q12*q23*q34);
  sub3:=64*q12*q23;
  qqf:=(sub1+sub2)^2-sub3;
  q13:=(q12-q23)^2;
  q24:=varp*(q23-q34)^2;
  if prnt then
  
   values:=<qqf,q13,q24>;
   DF:=DataFrame(<values>, columns=[`"Values Equations"`],rows=[`#1  QQF`,`#2  Q13`,cat(`#3  Q24 (`,varp,`)`)]);
   lens := [4 +8* max(op(length~(RowLabels(DF)))),4+ min(max( 10*(length~(values))),1000)];#op(length~(ColumnLabels(DF)0)
   Tabulate(DF,width=add(lens),widthmode = pixels,weights = lens);
  return qqf,q13,q24
  end if;
  return qqf,q13,q24
end proc:
> 

 q12:=1/2:q23:=9/10:q34:=25/26:q41:=9/130:#Cyclic quadrilateral
q12:=sqrt(17+a)/2:q23:=(r^2+t^2)^2/10:q34:=((a+b+c)^4/26):q41:=sqrt(17+b)/130:
> 

Q:=QQFProj(q12,q23,q34,q41,true):

Download 2024-12-01_Q_Data_Table_alpha_as_Greek_Letter.mw

A Christmas package needs to be wrapped......

Asked by: Alfred_F 450
volume recreational-mathematics
December 01 2024
1  2

An oddly shaped Christmas package is a collection of centrally stacked cube-shaped boxes with ever smaller sides. From bottom to top, the edge lengths of the stacked cubes run like the sequence of the reciprocals of the sequence of the square roots of the natural numbers. How high is the package? How much paper is needed to wrap the package? What is the total volume enclosed by all the packages?

Why when i take integral from whole equation is n...

Asked by: salim-barzani 1715
integration spam differential-equations
November 30 2024
0  1

why i take intgral from equation it must apply for each term but just by sign is show up how it will work?

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

declare(w(x, t))

w(x, t)*`will now be displayed as`*w

 (2)
> 

declare(f(x, t))

f(x, t)*`will now be displayed as`*f

 (3)
> 

NULL
> 

pde := diff(w(x, t), `$`(t, 2))-a*(diff(w(x, t), `$`(x, 4)))-b*(diff(w(x, t), `$`(x, 2), `$`(t, 2)))+(diff(w(x, t), t))*(diff(w(x, t), `$`(x, 2)))+2*(diff(w(x, t), x))*(diff(w(x, t), x, t)) = 0

diff(diff(w(x, t), t), t)-a*(diff(diff(diff(diff(w(x, t), x), x), x), x))-b*(diff(diff(diff(diff(w(x, t), t), t), x), x))+(diff(w(x, t), t))*(diff(diff(w(x, t), x), x))+2*(diff(w(x, t), x))*(diff(diff(w(x, t), t), x)) = 0

 (4)
> 

Y := w(x, t) = 2*(diff(ln(f(x, t)), `$`(x, 2)))

w(x, t) = 2*(diff(diff(f(x, t), x), x))/f(x, t)-2*(diff(f(x, t), x))^2/f(x, t)^2

 (5)
> 

L := eval(pde, Y)

2*(diff(diff(diff(diff(f(x, t), t), t), x), x))/f(x, t)-4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))/f(x, t)^2+4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2/f(x, t)^3-2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))/f(x, t)^2-4*(diff(diff(f(x, t), t), x))^2/f(x, t)^2+16*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), t))/f(x, t)^3-4*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^2-12*(diff(f(x, t), x))^2*(diff(f(x, t), t))^2/f(x, t)^4+4*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), t))/f(x, t)^3-a*(2*(diff(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x), x))/f(x, t)-12*(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x))*(diff(f(x, t), x))/f(x, t)^2+60*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(f(x, t), x))^2/f(x, t)^3-30*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(diff(f(x, t), x), x))/f(x, t)^2-240*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))^3/f(x, t)^4+240*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))*(diff(diff(f(x, t), x), x))/f(x, t)^3-20*(diff(diff(diff(f(x, t), x), x), x))^2/f(x, t)^2+720*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4/f(x, t)^5-540*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2/f(x, t)^4+60*(diff(diff(f(x, t), x), x))^3/f(x, t)^3-240*(diff(f(x, t), x))^6/f(x, t)^6)-b*(32*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^3+48*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))^2/f(x, t)^3+16*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(f(x, t), x), x))*(diff(diff(diff(f(x, t), t), t), x))*(diff(f(x, t), x))/f(x, t)^3+12*(diff(diff(f(x, t), x), x))^2*(diff(diff(f(x, t), t), t))/f(x, t)^3-48*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^4-240*(diff(f(x, t), x))^4*(diff(f(x, t), t))^2/f(x, t)^6+384*(diff(f(x, t), x))^3*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^5+48*(diff(f(x, t), x))^4*(diff(diff(f(x, t), t), t))/f(x, t)^5-144*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), x))^2/f(x, t)^4+32*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3+96*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))/f(x, t)^3-48*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))/f(x, t)^4-36*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), t))^2/f(x, t)^4-288*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))/f(x, t)^4-72*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^2/f(x, t)^4-144*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))^2/f(x, t)^4+288*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))^2/f(x, t)^5+2*(diff(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x), x))/f(x, t)+24*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), t), t), x), x))/f(x, t)^3-8*(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x))*(diff(f(x, t), x))/f(x, t)^2-12*(diff(diff(diff(diff(f(x, t), t), t), x), x))*(diff(diff(f(x, t), x), x))/f(x, t)^2-4*(diff(diff(diff(diff(diff(f(x, t), t), x), x), x), x))*(diff(f(x, t), t))/f(x, t)^2-16*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2-12*(diff(diff(diff(f(x, t), t), x), x))^2/f(x, t)^2+4*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(f(x, t), t))^2/f(x, t)^3-2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(diff(f(x, t), t), t))/f(x, t)^2-8*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^2)+(2*(diff(diff(diff(f(x, t), t), x), x))/f(x, t)-2*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))/f(x, t)^2-4*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+4*(diff(f(x, t), x))^2*(diff(f(x, t), t))/f(x, t)^3)*(2*(diff(diff(diff(diff(f(x, t), x), x), x), x))/f(x, t)-8*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))/f(x, t)^2+24*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^2/f(x, t)^3-6*(diff(diff(f(x, t), x), x))^2/f(x, t)^2-12*(diff(f(x, t), x))^4/f(x, t)^4)+2*(2*(diff(diff(diff(f(x, t), x), x), x))/f(x, t)-6*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))/f(x, t)^2+4*(diff(f(x, t), x))^3/f(x, t)^3)*(2*(diff(diff(diff(diff(f(x, t), t), x), x), x))/f(x, t)-6*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))/f(x, t)^2-2*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))/f(x, t)^2+12*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3-6*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+12*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), x))/f(x, t)^3-12*(diff(f(x, t), x))^3*(diff(f(x, t), t))/f(x, t)^4) = 0

 (6)
> 

numer(lhs(2*(diff(diff(diff(diff(f(x, t), t), t), x), x))/f(x, t)-4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))/f(x, t)^2+4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2/f(x, t)^3-2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))/f(x, t)^2-4*(diff(diff(f(x, t), t), x))^2/f(x, t)^2+16*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), t))/f(x, t)^3-4*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^2-12*(diff(f(x, t), x))^2*(diff(f(x, t), t))^2/f(x, t)^4+4*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), t))/f(x, t)^3-a*(2*(diff(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x), x))/f(x, t)-12*(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x))*(diff(f(x, t), x))/f(x, t)^2+60*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(f(x, t), x))^2/f(x, t)^3-30*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(diff(f(x, t), x), x))/f(x, t)^2-240*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))^3/f(x, t)^4+240*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))*(diff(diff(f(x, t), x), x))/f(x, t)^3-20*(diff(diff(diff(f(x, t), x), x), x))^2/f(x, t)^2+720*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4/f(x, t)^5-540*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2/f(x, t)^4+60*(diff(diff(f(x, t), x), x))^3/f(x, t)^3-240*(diff(f(x, t), x))^6/f(x, t)^6)-b*(32*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^3+16*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(f(x, t), x), x))*(diff(diff(diff(f(x, t), t), t), x))*(diff(f(x, t), x))/f(x, t)^3+384*(diff(f(x, t), x))^3*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^5+32*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3+96*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))/f(x, t)^3-48*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))/f(x, t)^4-72*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^2/f(x, t)^4-144*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))^2/f(x, t)^4+288*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))^2/f(x, t)^5+48*(diff(f(x, t), x))^4*(diff(diff(f(x, t), t), t))/f(x, t)^5-144*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), x))^2/f(x, t)^4-36*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), t))^2/f(x, t)^4+24*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), t), t), x), x))/f(x, t)^3-8*(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x))*(diff(f(x, t), x))/f(x, t)^2-12*(diff(diff(diff(diff(f(x, t), t), t), x), x))*(diff(diff(f(x, t), x), x))/f(x, t)^2-4*(diff(diff(diff(diff(diff(f(x, t), t), x), x), x), x))*(diff(f(x, t), t))/f(x, t)^2-16*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+4*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(f(x, t), t))^2/f(x, t)^3-2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(diff(f(x, t), t), t))/f(x, t)^2-8*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^2+48*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))^2/f(x, t)^3+12*(diff(diff(f(x, t), x), x))^2*(diff(diff(f(x, t), t), t))/f(x, t)^3-48*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^4-240*(diff(f(x, t), x))^4*(diff(f(x, t), t))^2/f(x, t)^6-288*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))/f(x, t)^4+2*(diff(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x), x))/f(x, t)-12*(diff(diff(diff(f(x, t), t), x), x))^2/f(x, t)^2)+(2*(diff(diff(diff(f(x, t), t), x), x))/f(x, t)-2*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))/f(x, t)^2-4*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+4*(diff(f(x, t), x))^2*(diff(f(x, t), t))/f(x, t)^3)*(2*(diff(diff(diff(diff(f(x, t), x), x), x), x))/f(x, t)-8*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))/f(x, t)^2+24*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^2/f(x, t)^3-6*(diff(diff(f(x, t), x), x))^2/f(x, t)^2-12*(diff(f(x, t), x))^4/f(x, t)^4)+2*(2*(diff(diff(diff(f(x, t), x), x), x))/f(x, t)-6*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))/f(x, t)^2+4*(diff(f(x, t), x))^3/f(x, t)^3)*(2*(diff(diff(diff(diff(f(x, t), t), x), x), x))/f(x, t)-6*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))/f(x, t)^2-2*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))/f(x, t)^2+12*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3-6*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+12*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), x))/f(x, t)^3-12*(diff(f(x, t), x))^3*(diff(f(x, t), t))/f(x, t)^4) = 0))*denom(rhs(2*(diff(diff(diff(diff(f(x, t), t), t), x), x))/f(x, t)-4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))/f(x, t)^2+4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2/f(x, t)^3-2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))/f(x, t)^2-4*(diff(diff(f(x, t), t), x))^2/f(x, t)^2+16*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), t))/f(x, t)^3-4*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^2-12*(diff(f(x, t), x))^2*(diff(f(x, t), t))^2/f(x, t)^4+4*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), t))/f(x, t)^3-a*(2*(diff(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x), x))/f(x, t)-12*(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x))*(diff(f(x, t), x))/f(x, t)^2+60*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(f(x, t), x))^2/f(x, t)^3-30*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(diff(f(x, t), x), x))/f(x, t)^2-240*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))^3/f(x, t)^4+240*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))*(diff(diff(f(x, t), x), x))/f(x, t)^3-20*(diff(diff(diff(f(x, t), x), x), x))^2/f(x, t)^2+720*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4/f(x, t)^5-540*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2/f(x, t)^4+60*(diff(diff(f(x, t), x), x))^3/f(x, t)^3-240*(diff(f(x, t), x))^6/f(x, t)^6)-b*(32*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^3+16*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(f(x, t), x), x))*(diff(diff(diff(f(x, t), t), t), x))*(diff(f(x, t), x))/f(x, t)^3+384*(diff(f(x, t), x))^3*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^5+32*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3+96*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))/f(x, t)^3-48*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))/f(x, t)^4-72*(diff(diff(f(x, t), x), 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t), x))^2/f(x, t)^3-6*(diff(diff(f(x, t), x), x))^2/f(x, t)^2-12*(diff(f(x, t), x))^4/f(x, t)^4)+2*(2*(diff(diff(diff(f(x, t), x), x), x))/f(x, t)-6*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))/f(x, t)^2+4*(diff(f(x, t), x))^3/f(x, t)^3)*(2*(diff(diff(diff(diff(f(x, t), t), x), x), x))/f(x, t)-6*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))/f(x, t)^2-2*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))/f(x, t)^2+12*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3-6*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+12*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), x))/f(x, t)^3-12*(diff(f(x, t), x))^3*(diff(f(x, t), t))/f(x, t)^4) = 0)) = numer(rhs(2*(diff(diff(diff(diff(f(x, t), t), t), x), x))/f(x, t)-4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))/f(x, t)^2+4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2/f(x, t)^3-2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))/f(x, t)^2-4*(diff(diff(f(x, t), t), x))^2/f(x, t)^2+16*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), t))/f(x, t)^3-4*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^2-12*(diff(f(x, t), x))^2*(diff(f(x, t), t))^2/f(x, t)^4+4*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), t))/f(x, t)^3-a*(2*(diff(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x), x))/f(x, t)-12*(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x))*(diff(f(x, t), x))/f(x, t)^2+60*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(f(x, t), x))^2/f(x, t)^3-30*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(diff(f(x, t), x), x))/f(x, t)^2-240*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))^3/f(x, t)^4+240*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))*(diff(diff(f(x, t), x), x))/f(x, t)^3-20*(diff(diff(diff(f(x, t), x), x), x))^2/f(x, t)^2+720*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4/f(x, t)^5-540*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2/f(x, t)^4+60*(diff(diff(f(x, t), x), x))^3/f(x, t)^3-240*(diff(f(x, t), x))^6/f(x, t)^6)-b*(32*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^3+16*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(f(x, t), x), x))*(diff(diff(diff(f(x, t), t), t), x))*(diff(f(x, t), x))/f(x, t)^3+384*(diff(f(x, t), x))^3*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^5+32*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3+96*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))/f(x, t)^3-48*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))/f(x, t)^4-72*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^2/f(x, t)^4-144*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))^2/f(x, t)^4+288*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))^2/f(x, t)^5+48*(diff(f(x, t), x))^4*(diff(diff(f(x, t), t), t))/f(x, t)^5-144*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), x))^2/f(x, t)^4-36*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), t))^2/f(x, t)^4+24*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), t), t), x), x))/f(x, t)^3-8*(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x))*(diff(f(x, t), x))/f(x, t)^2-12*(diff(diff(diff(diff(f(x, t), t), t), x), x))*(diff(diff(f(x, t), x), x))/f(x, t)^2-4*(diff(diff(diff(diff(diff(f(x, t), t), x), x), x), x))*(diff(f(x, t), t))/f(x, t)^2-16*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+4*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(f(x, t), t))^2/f(x, t)^3-2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(diff(f(x, t), t), t))/f(x, t)^2-8*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^2+48*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))^2/f(x, 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x))*(diff(f(x, t), x))/f(x, t)^2+4*(diff(f(x, t), x))^3/f(x, t)^3)*(2*(diff(diff(diff(diff(f(x, t), t), x), x), x))/f(x, t)-6*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))/f(x, t)^2-2*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))/f(x, t)^2+12*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3-6*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+12*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), x))/f(x, t)^3-12*(diff(f(x, t), x))^3*(diff(f(x, t), t))/f(x, t)^4) = 0))*denom(lhs(2*(diff(diff(diff(diff(f(x, t), t), t), x), x))/f(x, t)-4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))/f(x, t)^2+4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2/f(x, t)^3-2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))/f(x, t)^2-4*(diff(diff(f(x, t), t), x))^2/f(x, t)^2+16*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), t))/f(x, t)^3-4*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^2-12*(diff(f(x, t), x))^2*(diff(f(x, t), t))^2/f(x, t)^4+4*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), t))/f(x, t)^3-a*(2*(diff(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x), x))/f(x, t)-12*(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x))*(diff(f(x, t), x))/f(x, t)^2+60*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(f(x, t), x))^2/f(x, t)^3-30*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(diff(f(x, t), x), x))/f(x, t)^2-240*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))^3/f(x, t)^4+240*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))*(diff(diff(f(x, t), x), x))/f(x, t)^3-20*(diff(diff(diff(f(x, t), x), x), x))^2/f(x, t)^2+720*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4/f(x, t)^5-540*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2/f(x, t)^4+60*(diff(diff(f(x, t), x), x))^3/f(x, t)^3-240*(diff(f(x, t), x))^6/f(x, t)^6)-b*(32*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^3+16*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(f(x, t), x), x))*(diff(diff(diff(f(x, t), t), t), x))*(diff(f(x, t), x))/f(x, t)^3+384*(diff(f(x, t), x))^3*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^5+32*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3+96*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))/f(x, t)^3-48*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))/f(x, t)^4-72*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^2/f(x, t)^4-144*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))^2/f(x, t)^4+288*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))^2/f(x, t)^5+48*(diff(f(x, t), x))^4*(diff(diff(f(x, t), t), t))/f(x, t)^5-144*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), x))^2/f(x, t)^4-36*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), t))^2/f(x, t)^4+24*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), t), t), x), x))/f(x, t)^3-8*(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x))*(diff(f(x, t), x))/f(x, t)^2-12*(diff(diff(diff(diff(f(x, t), t), t), x), x))*(diff(diff(f(x, t), x), x))/f(x, t)^2-4*(diff(diff(diff(diff(diff(f(x, t), t), x), x), x), x))*(diff(f(x, t), t))/f(x, t)^2-16*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+4*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(f(x, t), t))^2/f(x, t)^3-2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(diff(f(x, t), t), t))/f(x, t)^2-8*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^2+48*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))^2/f(x, t)^3+12*(diff(diff(f(x, t), x), x))^2*(diff(diff(f(x, t), t), t))/f(x, t)^3-48*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^4-240*(diff(f(x, t), x))^4*(diff(f(x, t), t))^2/f(x, t)^6-288*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))/f(x, t)^4+2*(diff(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x), x))/f(x, t)-12*(diff(diff(diff(f(x, t), t), x), x))^2/f(x, t)^2)+(2*(diff(diff(diff(f(x, t), t), x), x))/f(x, t)-2*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))/f(x, t)^2-4*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+4*(diff(f(x, t), x))^2*(diff(f(x, t), t))/f(x, t)^3)*(2*(diff(diff(diff(diff(f(x, t), x), x), x), x))/f(x, t)-8*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))/f(x, t)^2+24*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^2/f(x, t)^3-6*(diff(diff(f(x, t), x), x))^2/f(x, t)^2-12*(diff(f(x, t), x))^4/f(x, t)^4)+2*(2*(diff(diff(diff(f(x, t), x), x), x))/f(x, t)-6*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))/f(x, t)^2+4*(diff(f(x, t), x))^3/f(x, t)^3)*(2*(diff(diff(diff(diff(f(x, t), t), x), x), x))/f(x, t)-6*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))/f(x, t)^2-2*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))/f(x, t)^2+12*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3-6*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+12*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), x))/f(x, t)^3-12*(diff(f(x, t), x))^3*(diff(f(x, t), t))/f(x, t)^4) = 0))

2*(diff(diff(diff(diff(f(x, t), t), t), x), x))*f(x, t)^6-4*(diff(diff(f(x, t), t), x))^2*f(x, t)^5-144*(diff(f(x, t), t))*(diff(f(x, t), x))^6-8*f(x, t)^4*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))+120*f(x, t)^3*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^2+8*f(x, t)^3*(diff(f(x, t), t))*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), x), x), x), x))+96*f(x, t)^3*(diff(diff(f(x, t), x), x))^2*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))+80*f(x, t)^3*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^2*(diff(diff(diff(f(x, t), x), x), x))-216*f(x, t)^2*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2-96*f(x, t)^2*(diff(f(x, t), t))*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), x), x), x))-288*f(x, t)^2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^3+360*f(x, t)*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4+144*f(x, t)^3*(diff(diff(f(x, t), t), x))^2*(diff(f(x, t), x))^2*b+48*f(x, t)^3*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), t), t), x))*b+240*f(x, t)^3*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), x), x), x))*a-720*f(x, t)^2*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4*a-48*f(x, t)^2*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^4*b+240*f(x, t)*(diff(f(x, t), t))^2*(diff(f(x, t), x))^4*b-40*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))-4*f(x, t)^4*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))+16*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), t))*f(x, t)^4-24*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))*(diff(diff(diff(f(x, t), x), x), x))-24*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))+36*f(x, t)^3*(diff(f(x, t), t))^2*(diff(diff(f(x, t), x), x))^2*b+540*f(x, t)^3*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2*a-60*f(x, t)^4*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*a-24*f(x, t)^4*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), t), t), x), x))*b+8*f(x, t)^5*(diff(f(x, t), x))*(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x))*b+8*f(x, t)^5*(diff(diff(diff(f(x, t), t), t), x))*(diff(diff(diff(f(x, t), x), x), x))*b-4*f(x, t)^4*(diff(f(x, t), t))^2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*b-12*f(x, t)^4*(diff(diff(f(x, t), x), x))^2*(diff(diff(f(x, t), t), t))*b-48*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))^2*b+12*f(x, t)^5*(diff(diff(f(x, t), x), x))*(diff(diff(diff(diff(f(x, t), t), t), x), x))*b+2*f(x, t)^5*(diff(diff(f(x, t), t), t))*(diff(diff(diff(diff(f(x, t), x), x), x), x))*b+16*f(x, t)^5*(diff(diff(f(x, t), t), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))*b+12*f(x, t)^5*(diff(f(x, t), x))*(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x))*a+4*f(x, t)^5*(diff(f(x, t), t))*(diff(diff(diff(diff(diff(f(x, t), t), x), x), x), x))*b+30*f(x, t)^5*(diff(diff(f(x, t), x), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))*a+144*f(x, t)^3*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))^2*b+48*f(x, t)^3*(diff(f(x, t), t))^2*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))*b+72*f(x, t)^3*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^2*b-288*f(x, t)^2*(diff(f(x, t), t))^2*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^2*b-384*f(x, t)^2*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^3*b+88*f(x, t)^3*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))-48*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*b-96*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))*b-32*f(x, t)^4*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))*(diff(diff(diff(f(x, t), x), x), x))*b-32*f(x, t)^4*(diff(f(x, t), t))*(diff(f(x, t), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))*b-48*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))*b-240*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))*a-16*f(x, t)^4*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))*b-2*f(x, t)^6*(diff(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x), x))*a-2*f(x, t)^6*(diff(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x), x))*b+12*f(x, t)^5*(diff(diff(diff(f(x, t), t), x), x))^2*b+20*f(x, t)^5*(diff(diff(diff(f(x, t), x), x), x))^2*a-60*f(x, t)^4*(diff(diff(f(x, t), x), x))^3*a+240*f(x, t)*(diff(f(x, t), x))^6*a-4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*f(x, t)^5+4*f(x, t)^5*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))-2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*f(x, t)^5-4*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))*f(x, t)^5+8*f(x, t)^5*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))-12*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), x), x))^2+4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2*f(x, t)^4-8*f(x, t)^4*(diff(f(x, t), t))*(diff(diff(diff(f(x, t), x), x), x))^2+4*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), t))*f(x, t)^4-12*(diff(f(x, t), x))^2*(diff(f(x, t), t))^2*f(x, t)^3+12*f(x, t)^3*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))^3+16*f(x, t)^3*(diff(f(x, t), x))^3*(diff(diff(diff(diff(f(x, t), t), x), x), x))-72*f(x, t)^2*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))^4+144*f(x, t)*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^5+288*f(x, t)^3*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))*b = 0

 (7)
> 

map(int, -8*f(x, t)^4*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))+120*f(x, t)^3*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^2+8*f(x, t)^3*(diff(f(x, t), t))*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), x), x), x), x))+96*f(x, t)^3*(diff(diff(f(x, t), x), x))^2*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))+80*f(x, t)^3*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^2*(diff(diff(diff(f(x, t), x), x), x))-216*f(x, t)^2*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2-96*f(x, t)^2*(diff(f(x, t), t))*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), x), x), x))-288*f(x, t)^2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^3+360*f(x, t)*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4+144*f(x, t)^3*(diff(diff(f(x, t), t), x))^2*(diff(f(x, t), x))^2*b+48*f(x, t)^3*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), t), t), x))*b+240*f(x, t)^3*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), x), x), x))*a-720*f(x, t)^2*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4*a-48*f(x, t)^2*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^4*b+240*f(x, t)*(diff(f(x, t), t))^2*(diff(f(x, t), x))^4*b-40*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))-4*f(x, t)^4*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))+16*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), t))*f(x, t)^4-24*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))*(diff(diff(diff(f(x, t), x), x), x))-24*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))+36*f(x, t)^3*(diff(f(x, t), t))^2*(diff(diff(f(x, t), x), x))^2*b+540*f(x, t)^3*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2*a-60*f(x, t)^4*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*a-24*f(x, t)^4*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), t), t), x), x))*b+8*f(x, t)^5*(diff(f(x, t), x))*(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x))*b+8*f(x, t)^5*(diff(diff(diff(f(x, t), t), t), x))*(diff(diff(diff(f(x, t), x), x), x))*b-4*f(x, t)^4*(diff(f(x, t), t))^2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*b-12*f(x, t)^4*(diff(diff(f(x, t), x), x))^2*(diff(diff(f(x, t), t), t))*b-48*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))^2*b+12*f(x, t)^5*(diff(diff(f(x, t), x), x))*(diff(diff(diff(diff(f(x, t), t), t), x), x))*b+2*f(x, t)^5*(diff(diff(f(x, t), t), t))*(diff(diff(diff(diff(f(x, t), x), x), x), x))*b+16*f(x, t)^5*(diff(diff(f(x, t), t), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))*b+12*f(x, t)^5*(diff(f(x, t), x))*(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x))*a+4*f(x, t)^5*(diff(f(x, t), t))*(diff(diff(diff(diff(diff(f(x, t), t), x), x), x), x))*b+30*f(x, t)^5*(diff(diff(f(x, t), x), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))*a+144*f(x, t)^3*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))^2*b+48*f(x, t)^3*(diff(f(x, t), t))^2*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))*b+72*f(x, t)^3*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^2*b-288*f(x, t)^2*(diff(f(x, t), t))^2*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^2*b-384*f(x, t)^2*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^3*b+88*f(x, t)^3*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))-48*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*b-96*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))*b-32*f(x, t)^4*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))*(diff(diff(diff(f(x, t), x), x), x))*b-32*f(x, t)^4*(diff(f(x, t), t))*(diff(f(x, t), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))*b-48*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))*b-240*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))*a-16*f(x, t)^4*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))*b+2*(diff(diff(diff(diff(f(x, t), t), t), x), x))*f(x, t)^6-4*(diff(diff(f(x, t), t), x))^2*f(x, t)^5-144*(diff(f(x, t), t))*(diff(f(x, t), x))^6-2*f(x, t)^6*(diff(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x), x))*a-2*f(x, t)^6*(diff(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x), x))*b+12*f(x, t)^5*(diff(diff(diff(f(x, t), t), x), x))^2*b+20*f(x, t)^5*(diff(diff(diff(f(x, t), x), x), x))^2*a-60*f(x, t)^4*(diff(diff(f(x, t), x), x))^3*a+240*f(x, t)*(diff(f(x, t), x))^6*a-4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*f(x, t)^5+4*f(x, t)^5*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))-2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*f(x, t)^5-4*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))*f(x, t)^5+8*f(x, t)^5*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))-12*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), x), x))^2+4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2*f(x, t)^4-8*f(x, t)^4*(diff(f(x, t), t))*(diff(diff(diff(f(x, t), x), x), x))^2+4*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), t))*f(x, t)^4-12*(diff(f(x, t), x))^2*(diff(f(x, t), t))^2*f(x, t)^3+12*f(x, t)^3*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))^3+16*f(x, t)^3*(diff(f(x, t), x))^3*(diff(diff(diff(diff(f(x, t), t), x), x), x))-72*f(x, t)^2*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))^4+144*f(x, t)*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^5+288*f(x, t)^3*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))*b = 0, x)

int(2*(diff(diff(diff(diff(f(x, t), t), t), x), x))*f(x, t)^6-4*(diff(diff(f(x, t), t), x))^2*f(x, t)^5-144*(diff(f(x, t), t))*(diff(f(x, t), x))^6-8*f(x, t)^4*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))+120*f(x, t)^3*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^2+8*f(x, t)^3*(diff(f(x, t), t))*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), x), x), x), x))+96*f(x, t)^3*(diff(diff(f(x, t), x), x))^2*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))+80*f(x, t)^3*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^2*(diff(diff(diff(f(x, t), x), x), x))-216*f(x, t)^2*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2-96*f(x, t)^2*(diff(f(x, t), t))*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), x), x), x))-288*f(x, t)^2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^3+360*f(x, t)*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4+144*f(x, t)^3*(diff(diff(f(x, t), t), x))^2*(diff(f(x, t), x))^2*b+48*f(x, t)^3*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), t), t), x))*b+240*f(x, t)^3*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), x), x), x))*a-720*f(x, t)^2*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4*a-48*f(x, t)^2*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^4*b+240*f(x, t)*(diff(f(x, t), t))^2*(diff(f(x, t), x))^4*b-40*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))-4*f(x, t)^4*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))+16*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), t))*f(x, t)^4-24*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))*(diff(diff(diff(f(x, t), x), x), x))-24*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))+36*f(x, t)^3*(diff(f(x, t), t))^2*(diff(diff(f(x, t), x), x))^2*b+540*f(x, t)^3*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2*a-60*f(x, t)^4*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*a-24*f(x, t)^4*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), t), t), x), x))*b+8*f(x, t)^5*(diff(f(x, t), x))*(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x))*b+8*f(x, t)^5*(diff(diff(diff(f(x, t), t), t), x))*(diff(diff(diff(f(x, t), x), x), x))*b-4*f(x, t)^4*(diff(f(x, t), t))^2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*b-12*f(x, t)^4*(diff(diff(f(x, t), x), x))^2*(diff(diff(f(x, t), t), t))*b-48*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))^2*b+12*f(x, t)^5*(diff(diff(f(x, t), x), x))*(diff(diff(diff(diff(f(x, t), t), t), x), x))*b+2*f(x, t)^5*(diff(diff(f(x, t), t), t))*(diff(diff(diff(diff(f(x, t), x), x), x), x))*b+16*f(x, t)^5*(diff(diff(f(x, t), t), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))*b+12*f(x, t)^5*(diff(f(x, t), x))*(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x))*a+4*f(x, t)^5*(diff(f(x, t), t))*(diff(diff(diff(diff(diff(f(x, t), t), x), x), x), x))*b+30*f(x, t)^5*(diff(diff(f(x, t), x), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))*a+144*f(x, t)^3*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))^2*b+48*f(x, t)^3*(diff(f(x, t), t))^2*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))*b+72*f(x, t)^3*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^2*b-288*f(x, t)^2*(diff(f(x, t), t))^2*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^2*b-384*f(x, t)^2*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^3*b+88*f(x, t)^3*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))-48*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*b-96*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))*b-32*f(x, t)^4*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))*(diff(diff(diff(f(x, t), x), x), x))*b-32*f(x, t)^4*(diff(f(x, t), t))*(diff(f(x, t), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))*b-48*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))*b-240*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))*a-16*f(x, t)^4*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))*b-2*f(x, t)^6*(diff(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x), x))*a-2*f(x, t)^6*(diff(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x), x))*b+12*f(x, t)^5*(diff(diff(diff(f(x, t), t), x), x))^2*b+20*f(x, t)^5*(diff(diff(diff(f(x, t), x), x), x))^2*a-60*f(x, t)^4*(diff(diff(f(x, t), x), x))^3*a+240*f(x, t)*(diff(f(x, t), x))^6*a-4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*f(x, t)^5+4*f(x, t)^5*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))-2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*f(x, t)^5-4*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))*f(x, t)^5+8*f(x, t)^5*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))-12*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), x), x))^2+4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2*f(x, t)^4-8*f(x, t)^4*(diff(f(x, t), t))*(diff(diff(diff(f(x, t), x), x), x))^2+4*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), t))*f(x, t)^4-12*(diff(f(x, t), x))^2*(diff(f(x, t), t))^2*f(x, t)^3+12*f(x, t)^3*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))^3+16*f(x, t)^3*(diff(f(x, t), x))^3*(diff(diff(diff(diff(f(x, t), t), x), x), x))-72*f(x, t)^2*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))^4+144*f(x, t)*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^5+288*f(x, t)^3*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))*b, x) = 0

 (8)

``

 (9)
 

``

Download int.mw

Unit conversion of results in the form of equations...

by: C_R 3612 Maple 2024
units convert
November 29 2024
1  0

As an enthusiast and frequent user of unit functionalities, I would like to suggest some improvements.

Example 1: 

Assume a quantity equation w = f(z) where we substitute z = 100*`&mu;m` (and probably other parameters with units) to obtain a numerical result.
After some simplifications the result is

w = 0.3365290139e-4*Unit('m')

w = 0.3365290139e-4*Units:-Unit(m)

 (1)

 

A result in this form is the most frequent physical quantity equation with units in use:

A physical quantity denoted by the name w that is equal to a numerical value times a physical unit.

In this form it is also the shortest way to define/name scientific constants, scientific and engineering parameters, and results for variables/unknowns.  


To better interpret the above result a conversion to micron is desirable. This unfortunately does not work with the context panel. Alternatively one could think of mapping a command onto the equation.
(Mapping a command is a good practice to threat the left-hand side and the right-hand side of an equation equally.)

map(convert, w = 0.3365290139e-4*Units:-Unit(m), units, micron)

Error, (in convert/units) unable to convert `1` to `micron`

  

This however does not work, since the left-hand side does not contain the dimension length, but only the name w of the physical quantity.  

A way to convert is:

lhs(w = 0.3365290139e-4*Units:-Unit(m)) = convert(rhs(w = 0.3365290139e-4*Units:-Unit(m)), units, micron)

w = 33.65290139*Units:-Unit(micron)

 (2)

For a single result this might be acceptable, but for a list of results this not practical.

In any case not being capable to apply to an equation the same operation to both sides bares the risks of introducing errors.

NULL

Example 2: 

More complicated are results of this kind

NULL

w((1/10000)*Unit('m')) = 0.3365290139e-4*Unit('m')

w((1/10000)*Units:-Unit(m)) = 0.3365290139e-4*Units:-Unit(m)

 (3)

A way to convert this to w(100*`&mu;m`) = 33.65290139*`&mu;m`:

w(convert(op(lhs(w((1/10000)*Units:-Unit(m)) = 0.3365290139e-4*Units:-Unit(m))), units, micron)) = convert(rhs(w((1/10000)*Units:-Unit(m)) = 0.3365290139e-4*Units:-Unit(m)), units, micron)

w(100*Units:-Unit(micron)) = 33.65290139*Units:-Unit(micron)

 (4)

This is too complicated.

Instead, eval with a manually entered conversion can be used for this

eval(w(100*Units:-Unit(micron)) = 33.65290139*Units:-Unit(micron), Unit('m') = 10^6*Unit('`&mu;m`'))

w(100*Units:-Unit(micron)) = 33.65290139*Units:-Unit(micron)

 (5)

However, this is old style: The way we had to work before the introduction of the unit package.

 

In other areas Maples unit conversion functionalities are more advanced.

Plotting with units for example has been improved to the point where unit conversion errors of quantity expressions are almost impossible (in contrast to numerical-value expressions): The user can specify the units to display and the numerical values of the physical quantities are converted accordingly.

 

S1: To catch up with that improvement, conversion of the results as in Example 1 in the form of quantity equations would be desirable as well.

 

Other desirable unit conversions of quantity expressions are

 

• 

S2: Right click (or select and right click) a unit in Maple output and conversion to a new unit with the context panel (try it with one of the above outputs: nothing happens).

• 

S3: Replacement of a unit by a desired unit of the same dimension (Example 2).
• 

S4: Replacement of a unit by conversion to a new equivalent unit (e.g.: "&lobrk;(m kg)/(s^3 A)&robrk; to V/(m)") matching the pattern of the unit but not necessarily the pattern of the underlying Unit commands (for this subs can be used already).

 

For all suggestions, it is important that the physical quantity to be converted does not change, i.e. if a unit is changed, the numerical value of the physical quantity is changed accordingly.

 

Download Unit_conversion_in_quantity_expressions.mw

I don't like indenting input text...

Asked by: michele 90
input 2dmath
November 29 2024
2  11

With the latest version of Maple I get an indenting space when I click "Shift+Enter".
For example 

But I don't like it: suggestion? Thanks

How to get this recursive sequence of A[n] (warnin...

Asked by: Aixleft math 120
rsolve recurrence
November 26 2024
1  4

Hi, how to rsolve this recursive sequence auto? 

The manual calculation is taking the reciprocal of both sides of the equation, and then do some simple calculations to get the answer:1/(3·2^n-5).

> 

restart; A := 'A'; A[n] := `assuming`([rsolve({A[1] = 1, A[n+1] = A[n]/(5*A[n]+2)}, A[n])], [n::posint]); A[n] := simplify(%); simplify(subs(n = 1, %))

Error, recursive assignment

  

A

  

Error, (in simplify/table) too many levels of recursion

  

Download ask_recrusive_sequence_of_A[n].mw

Why 2d input sometimes becomes roman...

Asked by: C_R 3612
interface 2dmath
November 25 2024
4  10

Something has changed in the past weeks (not sure for how long) and I have not figured out what exactly.

Probably it is me doing something differently while editing an input line. Below is an example where the name data is not italic any more

Anybody else experiencing the same?

My interface seetings:

Error in NLPSolve and recursion for parameter fitt...

Asked by: countryplaza 10
November 24 2024
2  4

Hello to whomever this may concern. I am curently trying to estimate parameters and initial conditions for a system of ODEs. I have taken inspiration from the code given by Robert J. Lopez. I am having issues with minimizing the SSE (sum of squared errors) which I named as a procedure using the NLPSolve command from the Optimization package. It returns an error saying there are too many levels of recursion, which I do not understand where it is coming from or how to solve the issue and I was hoping to get an explination on how to solve it.

Below is the code up until the error. Any help or guidance would be greatly appreciated.

Parameter_estimation.mw

problem in replacing mu in equation ?...

Asked by: salim-barzani 1715
2dmath subscript indexed
November 24 2024
0  4

when i replace mu=0 in my equation mu[3] and mu[4] also become zero why ?

> 

restart
> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

NULL
> 

B[1] := 0; mu := 0

0

  

0

 (2)
> 

U1 := lambda*(1+sqrt(-lambda)*(cosh(xi*sqrt(-lambda))*B[2]+sinh(xi*sqrt(-lambda))*B[1])*`&+-`(sqrt(lambda/(lambda^2*B[1]^2-lambda^2*B[2]^2-mu^2))))*beta[0]*exp(I*(d*x+e*y+f*t^beta/beta))/(B[1]*cosh(xi*sqrt(-lambda))*lambda+B[2]*sinh(xi*sqrt(-lambda))*lambda+mu)

(1+(-lambda)^(1/2)*cosh(xi*(-lambda)^(1/2))*B[2]*`&+-`((-1/(lambda*B[2]^2))^(1/2)))*beta[0]*exp(I*(d*x+e*y+f*t^beta/beta))/(B[2]*sinh(xi*(-lambda)^(1/2)))

 (3)
> 

NULL
> 

V1 := -mu[4]*b*lambda^2*(1+sqrt(-lambda)*(cosh(xi*sqrt(-lambda))*B[2]+sinh(xi*sqrt(-lambda))*B[1])*`&+-`(sqrt(lambda/(lambda^2*B[1]^2-lambda^2*B[2]^2-mu^2))))^2*beta[0]^2/((B[1]*cosh(xi*sqrt(-lambda))*lambda+B[2]*sinh(xi*sqrt(-lambda))*lambda+mu)^2*a*mu[3])

Error, numeric exception: division by zero

  

Download tester.mw

Find ODE solution with condition parameter ?...

Asked by: salim-barzani 1715
ode assumptions homework
November 23 2024
0  12

How we can calculate solution of this ODE by give assumption to the equation , we have otehr case too, like lambda>0&mu<0

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