Hi, am trying to differentiate the following eq w.r.t t2 and N. But in t2 I am getting zero and in wrt N, an Error (non-algebraic expressions cannot be differentiated). But according to the article, I am following expression should come.

I am differentiating following

TCS := proc (N, T, m, n) options operator, arrow; piecewise(M <= t__3 and N <= t__4, TCS__1, M <= t__3 and t__4 < N, TCS__2, t__3 <= M and N <= t__4, TCS__3, `t__3 ` <= M and t__4 < N, TCS__4) end proc

ode5 := diff(proc (N, T, m, n) options operator, arrow; piecewise(M <= t__3 and N <= t__4, TCS__1, M <= t__3 and t__4 < N, TCS__2, t__3 <= M and N <= t__4, TCS__3, `t__3 ` <= M and t__4 < N, TCS__4) end proc, t__2) = 0

ode6 := diff(proc (N, T, m, n) options operator, arrow; piecewise(M <= t__3 and N <= t__4, TCS__1, M <= t__3 and t__4 < N, TCS__2, t__3 <= M and N <= t__4, TCS__3, `t__3 ` <= M and t__4 < N, TCS__4) end proc, N) = 0

Error, non-algebraic expressions cannot be differentiated
 

following are the pre-requisite to use above (also in the attachment doubt_2.mw)

i__m1(t) = ((-c*t^2*theta__m^2+b*t*theta__m^2+2*c*t*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t)*a*N^alpha*(lambda-1)/theta__m^3-(-b*theta__m+theta__m^2-2*c)*a*N^alpha*(lambda-1)/theta__m^3)*exp(-theta__m*t)

i__m2(t) = (-(-c*t^2*theta__m^2+b*t*theta__m^2+2*c*t*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t)*a*N^alpha/theta__m^3+(-c*t__2^2*theta__m^2+b*t__2*theta__m^2+2*c*t__2*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__2)*a*N^alpha/theta__m^3)*exp(-theta__m*t)

TC__m := A__m/(t__1+t__2)+(int(h__m*(i__m*t+1)*i__m1(t), t = 0 .. t__1))*(int(h__m*(i__m*t+1)*i__m2(t), t = 0 .. t__2))+P__m*I__om*m*(-(1/3)*a*c*N^alpha*M^3+(1/2)*a*b*N^alpha*M^2+a*N^alpha*M)/(t__1+t__2)+C__m*theta__m*(int(i__m1(t), t = 0 .. t__1)+int(i__m2(t), t = 0 .. t__2))/(t__1+t__2)

i__d(t) = (-(-c*t^2*theta__d^2+b*t*theta__d^2+2*c*t*theta__d-b*theta__d+theta__d^2-2*c)*a*N^alpha*exp(theta__d*t)/theta__d^3+(-c*t__3^2*theta__d^2+b*t__3*theta__d^2+2*c*t__3*theta__d-b*theta__d+theta__d^2-2*c)*a*N^alpha*exp(theta__d*t__3)/theta__d^3)*exp(-theta__d*t)

TC__d1 := A__d*m/(t__1+t__2)+m*(int(h__d*(i__d*t+1)*i__d(t), t = 0 .. t__3))/(t__1+t__2)+P__d*I__OD*m*n*(-(1/3)*a*c*N^alpha*N^3+(1/2)*a*b*N^alpha*N^2+a*N^alpha*N)/(t__1+t__2)+P__m*theta__m*m*(int(i__d(t), t = 0 .. t__3))/(t__1+t__2)+P__m*I__c*m*(int(i__d(t), t = M .. t__3))/(t__1+t__2)-P__d*I__e*m*(-(1/3)*a*c*N^alpha*M^3+(1/2)*a*b*N^alpha*M^2+a*N^alpha*M)/(t__1+t__2)

TC__d2 := A__d*m/(t__1+t__2)+m*(int(h__d*(i__d*t+1)*i__d(t), t = 0 .. t__3))/(t__1+t__2)+P__d*I__OD*m*n*(-(1/3)*a*c*N^alpha*N^3+(1/2)*a*b*N^alpha*N^2+a*N^alpha*N)/(t__1+t__2)+P__m*theta__m*m*(int(i__d(t), t = 0 .. t__3))/(t__1+t__2)-P__d*I__e*m*(-(1/4)*a*c*N^alpha*t__3^4+(1/3)*a*b*N^alpha*t__3^3+(1/2)*a*N^alpha*t__3^2+M-t__3-(1/3)*a*c*N^alpha*t__3^3+(1/2)*a*b*N^alpha*t__3^2+a*N^alpha*t__3)/(t__1+t__2)

i__r(t) = (-(-c*t^2*theta__r^2+b*t*theta__r^2+2*c*t*theta__r-b*theta__r+theta__r^2-2*c)*a*N^alpha*exp(theta__r*t)/theta__r^3+(-c*t__4^2*theta__r^2+b*t__4*theta__r^2+2*c*t__4*theta__r-b*theta__r+theta__r^2-2*c)*a*N^alpha*exp(theta__r*t__4)/theta__r^3)*exp(-theta__r*t)

TC__r1 := A__r*m*n/(t__1+t__2)+m*n*(int(h__r*(i__r*t+1)*i__r(t), t = 0 .. t__4))/(t__1+t__2)+P__d*theta__r*m*n*(int(i__r(t), t = 0 .. t__4))/(t__1+t__2)+P__d*I__c*m*n*(int(i__r(t), t = N .. t__4))/(t__1+t__2)-P__r*I__e*m*n*(-(1/4)*a*c*N^alpha*N^4+(1/3)*a*b*N^alpha*N^3+(1/2)*a*N^alpha*N^2)/(t__1+t__2)

TC__r2 := A__r*m*n/(t__1+t__2)+m*n*(int(h__r*(i__r*t+1)*i__r(t), t = 0 .. t__4))/(t__1+t__2)+P__d*theta__r*m*n*(int(i__r(t), t = 0 .. t__4))/(t__1+t__2)-P__r*I__e*m*n*(-(1/4)*a*c*N^alpha*t__4^4+(1/3)*a*b*N^alpha*t__4^3+(1/2)*a*N^alpha*t__4^2+N-t__4-(1/3)*a*c*N^alpha*t__4^3+(1/2)*a*b*N^alpha*t__4^2+a*N^alpha*t__4)/(t__1+t__2)

TCS__1 := TC__m+TC__d1+TC__r1

TCS__2 := TC__m+TC__d1+TC__r2

TCS__3 := TC__m+TC__d2+TC__r1

TCS__4 := TC__m+TC__d2+TC__r2

Thanks in advance.

Hi,

I want to solve an equation(see the attached file) numerically, find  values of M that satisfy this equation and then plot the curve of M versus sigmai for those values of M that satisfy the mentioned equation. How can I do that with Maple?

eq.mw

MacDude posted a worksheet for creating help files using the makehelp command that I found very useful.  However, his worksheet created a table of contents that organized the command help pages under a single folder.  I wanted to create a help file table of contents with the commands organized into sub-folders under the main application folder. ie. Package Name,Folder Name, command. The help page for makehelp is not very informative; in particular the example that shows (purportedly) how to override the existing help pages with your own help file is very misleading.  Also, the description of the parameters to the browser option of the makehelp command is too vague. I needed an error message to tell me that the browser option expects parameters in the form List(Name,String).  In the end, I was able to get a folder/sub-folder structure using a structure [`Folder Name`,`Subfolder Name`,"Command"].  Sub-folders are sorted alphabetically. If anyone has a need, the attached worksheet shows how I created the table of contents structure. 

helpcode.mw

In the OrthogonalExpansions package, how can I change the summation variable to be n instead of i?

doubt_1.mw

Hi, I am trying to solve two simultaneous equations (for t1) they are as follows-

eq 1

i__m2(0) = (-(-b*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`+`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2-2*c)*exp(0)*a*N^alpha/`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^3+(-c*t__2^2*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2+b*t__2*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2+2*c*t__2*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`-b*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`+`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2-2*c)*exp(`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`*t__2)*a*N^alpha/`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^3)*exp(0)

eq 2

i__m1(t__1) = ((-c*t__1^2*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2+b*t__1*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2+2*c*t__1*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`-b*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`+`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2-2*c)*exp(`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`*t__1)*a*N^alpha*(lambda-1)/`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^3-(-b*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`+`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2-2*c)*a*N^alpha*(lambda-1)/`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^3)*exp(-`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`*t__1)

rhs(i__m2(0) = (-(-b*theta__m+theta__m^2-2*c)*exp(0)*a*N^alpha/theta__m^3+(-c*t__2^2*theta__m^2+b*t__2*theta__m^2+2*c*t__2*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__2)*a*N^alpha/theta__m^3)*exp(0)) = rhs(i__m1(t__1) = ((-c*t__1^2*theta__m^2+b*t__1*theta__m^2+2*c*t__1*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__1)*a*N^alpha*(lambda-1)/theta__m^3-(-b*theta__m+theta__m^2-2*c)*a*N^alpha*(lambda-1)/theta__m^3)*exp(-theta__m*t__1))

solve({-(-b*theta__m+theta__m^2-2*c)*a*N^alpha/theta__m^3+(-c*t__2^2*theta__m^2+b*t__2*theta__m^2+2*c*t__2*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__2)*a*N^alpha/theta__m^3 = ((-c*t__1^2*theta__m^2+b*t__1*theta__m^2+2*c*t__1*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__1)*a*N^alpha*(lambda-1)/theta__m^3-(-b*theta__m+theta__m^2-2*c)*a*N^alpha*(lambda-1)/theta__m^3)*exp(-theta__m*t__1)}, [t__1]);
Warning, solutions may have been lost
 

Can someone, please help. Thanks in advance.

Any idea why a similar indexing call to an Array and a Matrix gives different "orientations"?

The indexing call [1..2,1] to a Matrix gives a a column Vector, while a similar call to an Array gives a (row) Array. So somehow the Array call gives a transpose of the original.

MatrixVsArray.mw

I have used maple to solve a system of differential equations. However, I need to do the same in R. The problem is that when I use the same parameter values as used in maple to R, I don't get the same plots. Can someone assist wrt? 

The definition 
a:=ModularSquareRoot(10,11)
returns
Error, ... because no numbers in Z11 have the square equal to 10. I need, in a procedure, to prevent the error, I mean something like this:
if a<>ERROR then b:=b+1 else c:=c+1 end if
Any suggestions? Thanks

Dear maple users,

Greetings.

JVB.mw
 

Download JVB.mw

How to obtain a solution for various values of "ax"

waiting for your reply.

how can i plot the relation betwen x and B[k] from result of itterition in this work sheetx_phi.mw

Download x_phi.mw

I can't figure out how to write a program to work out the classification of a conic and if it is a degenerate given a data file.

So far I have programed the following which reads the conic coefficients (a,h,b,f,g,c) and displays it as an equation: 

conic :=proc(a,h,b,f,g,c)
local C;
C:= a*x^2+h*x*y+b*y^2+f*x+g*y+c=0;
end proc:

Can anyone help me work this out

According to Wikipedia, Abel's first order odes have general analytical solutions, due to "Panayotounakos, Dimitrios E.; Zarmpoutis, Theodoros I. (2011)" where the claim is that, if I understand it right, all Abel ode's can be solved analytically.

https://en.wikipedia.org/wiki/Abel_equation_of_the_first_kind

"Construction of Exact Parametric or Closed Form Solutions of Some Unsolvable Classes of Nonlinear ODEs (Abel's Nonlinear ODEs of the First Kind and Relative Degenerate Equations)"

Maple is very good on solving ODE's, but some Abel ode's it can not solve. For example

restart;
ode:=diff(y(t),t)= y(t)^3+exp(-5*t);#_Abel
ode:=diff(y(x),x) = (1+x^3*y(x))*y(x)^2;#_Abel
ode:=diff(y(x),x) = y(x)^2-a*x*(1-x^(n-1))*y(x)^3;#_Abel
ode:=diff(y(x),x) = a*y(x)^2+x*y(x)^3*(b+c*x^(n-1));#_Abel
ode:=diff(y(x),x) = f0(x)+f1(x)*y(x)+f2(x)*y(x)^2+f3(x)*y(x)^3;#_Abel
ode:=(tan(x)*sec(x)-2*y(x))*diff(y(x),x)+sec(x)*(1+2*y(x)*sin(x)) = 0;#_Abel, `2nd type`, `class A`
ode:=x*(a+y(x))*diff(y(x),x)+b*x+c*y(x) = 0; #[_Abel, `2nd type`, `class B`]
ode:=(g0(x)+y(x)*g1(x))*diff(y(x),x) = f0(x)+f1(x)*y(x)+f2(x)*y(x)^2+f3(x)*y(x)^3;#_Abel, `2nd type`, `class C`

etc..

All the above Abel ode's are from Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960

I am just asking what is the status of this. Is it true there is now a method to solve all these exactly and may be Maple's implementation is not in yet for this? 

btw, I found the description of solution methods in https://fr.maplesoft.com/support/help/Maple/view.aspx?path=odeadvisor/Abel much easier to follow to learn how to solve Abel ode's. That paper mentioned on Wikipeida, I had hard time following after the 3rd page. (need more time to study it).

Could someone please comment on the status of solving Abel's first order ODE's in Maple and if it possible now to solve them all analytically?

Dear friends, 

I have to select the last element of a remember table T from a recursive procedure. I've tried 

with(ListTools): 

SelectLast(T); 

as this command works with rtables, as it is stated in Maple's online help page. However I receive no result. 

Can you please tell me how to obtain a correct result? 

Many thanks for the help. 

I've got a question regarding sum of matrix or arrays.

My problem is that sum of the values of the maxtrices is not calculated, but shown as a sum with the '+' sign. I have tried to recreate the problem with an easier example, but so far I have not managed to do so.

Before posting the whole program, I'd like to post it as a question, if someone has an idea about how I could get an evaluation of the matrix.

Here's a screenshot.

Why when trying to substitute a term in denominator, subs does not work, when this term is product. But it works when this term is single variable?

subs((x*y)=t,1/(x*y));

does not work. i.e. it does not return 1/t

But this works

subs(z=t,1/z);

and returns 1/t

algsubs does not work either on the first example above. 

Just wondering why, that is all.