I have tried to use Maple to solve ordinary differential equations but i have this error. Could you please help me to fix this problem

> eq1 := diff(v1(t), t) = v2(t);
> eq2 := diff(v2(t), t) = -v1(t)+(3*(v1(t)^2-1))*v2(t);
> init1 := v1(0) = 2;
> init2 := v2(0) = 0;
> with(DEtools);
> DEplot({eq1, eq2}, [v1(t), v2(t)], 0 .. 3*Pi, {[0, 0, 0]}, scene = [v1, v2], stepsize = .1);

Error, (in DEtools/DEplot/direction) division by zero

thank you

b := 1;

h := 1;

A := b*h;

E := 210*10^9;

qr := 100;

Dp := (1/12)*E*b*h^3;

R := 20;

teta := 3;

sys1 := {(E.A+Dp/R^2)*(diff(u(t), `$`(t, 2))) = -E*A*(diff(w(t), t))/R+Dp*(diff(w(t), `$`(t, 3)))/R, -Dp*(diff(w(t), `$`(t, 4))) = E*A*(diff(u(t), t))/R-Dp*(diff(u(t), `$`(t, 3)))/R+E*A/R-100};

dsolve(sys1);

#THİS GAVE ME THE RESULTS LİKE THAT:

{u(t) = (1/4801)*_C3*(-1+sqrt(4801))^(3/2)*exp(-(1/20)*sqrt(-1+sqrt(4801))*t)-(1/4801)*_C4*(-1+sqrt(4801))^(3/2)*exp((1/20)*sqrt(-1+sqrt(4801))*t)-(1/4801*I)*_C5*(1+sqrt(4801))^(3/2)*exp(-(1/20*I)*sqrt(1+sqrt(4801))*t)-(1/4801)*_C6*(-1+sqrt(4801))^(3/2)*exp((1/20)*sqrt(-1+sqrt(4801))*t)+(1/4801)*_C3*sqrt(-1+sqrt(4801))*exp(-(1/20)*sqrt(-1+sqrt(4801))*t)-(1/4801)*_C4*sqrt(-1+sqrt(4801))*exp((1/20)*sqrt(-1+sqrt(4801))*t)+(1/4801*I)*_C5*sqrt(1+sqrt(4801))*exp(-(1/20*I)*sqrt(1+sqrt(4801))*t)-(1/4801)*_C6*sqrt(-1+sqrt(4801))*exp((1/20)*sqrt(-1+sqrt(4801))*t)-(104999999/105000000)*t+_C1, w(t) = _C2+_C3*exp(-(1/20)*sqrt(-1+sqrt(4801))*t)+_C4*exp((1/20)*sqrt(-1+sqrt(4801))*t)+_C5*exp(-(1/20*I)*sqrt(1+sqrt(4801))*t)+_C6*exp((1/20)*sqrt(-1+sqrt(4801))*t)}

#SO THERE ARE 6 UNKOWN(C1...C6) SO I NEED 6 CONDITION. MY BOUNDRY CONDITIONS:

bs := u(0) = 0, (D(u))(0) = 0, w(0) = 0, (D(w))(0) = 0, w(teta) = 0, (D(w))(teta) = 0;

> r := dsolve({bs, sys1});
%;
Error, (in dsolve) invalid arguments; expected an equation, or a set or list of them, received: {{-17500000000*(diff(diff(diff(diff(w(t), t), t), t), t)) = 10500000000*(diff(u(t), t))-875000000*(diff(diff(diff(u(t), t), t), t))+10499999900, 210043750000*(diff(diff(u(t), t), t)) = -10500000000*(diff(w(t), t))+875000000*(diff(diff(diff(w(t), t), t), t))}}
>

I tried to change the equations row. But ı dont understand where something wrong.I tried so many times. May u please find where ıt is wrong? 

Hello,

I would like to know whether it is possible to change the color of animations that have already been produced and assigned to a variable.

Let's take for example

P := plots:-animate(plot, [sin(x+t), x = -Pi .. Pi], t = -Pi .. Pi, frames = 8)

is there a command to change the color of the curve AFTER it has been produced?

The calculus to generate all my plots took 4 hours so I would like not to have them calculated again.

Thx

How can I typeset this in Maple? A ket with a 2 element column vector in it, but without the vector brakets. Like this:

| x over y >

Thanks

AOA... Pl correct it

Help.mw

can we load part of a package not the package whole !? for example from physics package i only need diff tool not all of the package tools,can i do sth for that !? 

restart:

Eq1:=diff(psi(y),y$4)-diff(psi(y),y$2)=0;

dsolve({Eq1});

bcs:=psi(h1)=F,D(psi)(h1)=-1,psi(h2)=-F,D(psi)(h2)=-1;

dsolve({Eq1,bcs});

Error, (in dsolve) found differentiated functions with same name but depending on different arguments in the given DE system: [{psi(h1), psi(h2), psi(y)}, {psi(h2), psi(y)}]

Any suggestion?

Cheers!

Dear all;

Please see only the last lines of this procedure,

1)I ask if this procedure give an output epsilon(x0,h). Really, I need your help. Thanks.

2) Can we plot epsilon(x0,h), versus h

> heun := proc (x0, h)

local x, y, i, N, k, f, ode, k1, k2, x1, x2, y1, y2;

f :=(x,y)-> 1/(1+cos(y)) ;

ode := diff(y(x), x) = f(x, y);

N := round((1/2)*x0/h);

y2 := Array(0 .. N);

x2 := Array(0 .. N);

y1 := Array(0 .. 2*N);

x1 := Array(0 .. 2*N);

x2[0] := 0; y2[0] := (1/4)*Pi;

for i from 0 to N-1 do

x1[2*i+2] := (2*i+2)*h;  k1[1] := f(x1[2*i], y1[2*i]); 

k1[2] := f(x1[2*i]+h, y1[2*i]+h*k1[1]);

y1[2*i+2] := y1[2*i]+(1/2)*h*(k1[1]+k1[2]);

x2[i+1] := (2*i+2)*h;

k2[1] := f(x2[i], y2[i]);

k2[2] := f(x2[i]+2*h, y2[i]+2*h*k2[1]);

y2[i+1] := y2[i]+h*(k2[1]+k2[2])

end do;

return firstresulat = evalf([seq([x2[i], y2[i]], i = 0 .. N)]);

return secondresulat =evalf([seq([x1[2*i], y1[2*i]], i = 0 .. N)]);

epsilon:=(x0,h)->add((firsttest[i][2]-secondtest[i][2])^2 , i=1..round(x0/(2*h))+1)

end proc;

how maple calculate exp(x) with e.g. 100000 decimal numbers

a divsion of the series x^k/k! with e.g. 1/25000!/25001 lasts longer than the exp(1.xx) calculation

is there a faster way to calculate exp(x) than with the x^k/k! series

thanks

I've been poking around with convolutions on Maple, and some weird behavior came up---if I let it compute the convolution of a piecewise function, then take the convolution of that, it comes out differently than if I enter a function from scratch as the middle step---file attached (PiecewiseProblem.mw).  I'm not really a Maple pro, so am I'm doing something crazy here?

Thanks!

hello, 

so i've been having trouble with this one for a while. I think i'm just missing something simple.. maybe yous could help.

all we have to do is to write a maple procedure that takes an integer N and a boolean function F as in14 as arguments, returns nothing, and plots a square N N lattice of points, coloring the points (i; j) with F(i; j) true in red and the other ones blue.

thaaaanks.

Dear all,

Thank you for your Help.

h: stepsize;

x in [0,x0];

I give all the step of my code, but I think there is a mistake. I wait for your Help.

I would like to compute the error between  Method Huen with step size h and step size 2h using the definition of epsilon given below:

 ## The error written epsilon(x0,h)= sqrt(1/(N+1) * sum_i=0^N  (y_i^{2h}-y_(2i)^h)^2 ), where y_i^(2h) is the approximation of y(i*2*h).

 ## We want : loglog epsilon versus h.

  epsilon:=(x0,h)->sqrt( 1/(N+1)*add( (Heun1(f,x0,i)-Heun2(f,x0,i))^2,i=0..N ) );

  f:=(x,y)=1/(1+cos(y)); 

  ode:=diff(y(x),x)=f(x,y);

ic:=y(0)=1;  h:=x0/(2*N);

## Method Heun with step size 2h

> Heun1 := proc (f, x0,)

local x, y, i, h, k;

y := Array(0 .. N);

x := Array(0 .. N);

h := evalf((1/2)*x0/N);

x[0] := 0;

y[0] := 1;

for i from 0 to N do

x[i+1] := (2*i+2)*h;

k[1] := f(x[i], y[i]);

k[2] := f(x[i]+h, y[i]+h*k[1]);

y[i+1] := y[i]+h*((1/2)*k[1]+(1/2)*k[2]);

end do;

[seq([x[i], y[i]], i = 0 .. N)];

end proc;

### Now Heun with step size h  ( the same h)

> Heun2 := proc (f, x0,)

local x, y, i, h, k;

y := Array(0 .. N);

x := Array(0 .. N);

h := evalf((1/2)*x0/N);

x[0] := 0;

y[0] := 1;

for i from 0 to N do

x[i+1] := (i+1)*h;

k[1] := f(x[i], y[i]);

k[2] := f(x[i]+h, y[i]+h*k[1]);

y[i+1] := y[i]+h*((1/2)*k[1]+(1/2)*k[2]);

end do;

[seq([x[2*i], y[2*i]], i = 0 .. N)];

end proc;

Thanks you for your help.

> with(DETools);
> eq1 := diff(y(t), t) = v(t);
d
--- y(t) = v(t)
dt
> eq2 := diff(v(t), t) = -3*v(t)+10*y(t);
d
--- v(t) = -3 v(t) + 10 y(t)
dt
> phaseportrait([eq1, eq2], [y, v], t = 0 .. 10, [[y(0) = 0, v(0) = 1]], y = -10 .. 10, v = -10 .. 10, linecolor = blue);

why my phase portrait not working

I want to define the budget set of a consumer, which consists of an horizontal, slant and vertical line segments. How can I define and plot the budget set?

I find this a little frustrating as I learn Maple, so I think there is a better way to handle this.

I find myself having to keep wrapping expressions with evalf() in order to compare them, since when I use a constant such as Pi in these expressions and then compare them,  Maple complains.

In a large program, one does not know if an expression contains Pi or not beforehand, so is one really supposed to convert every expression to float just in case they might need to compare 2 expressions? 

Let me explain with simple example:

x:=1.2;  #it does not matter if this was 12/10 or 1.2, same error will result.
y:=Pi/3;
if x<y then
   print("x<y");
else
   print("x>=y");
fi;

The above gives the error "Error, cannot determine if this expression is true or false: 1.2<(1/3)*Pi"

So I changed the y assignment above to y:=evalf(Pi/3); or evalf(Pi)/3; and now Maple is happy.

But this for me looks awkward. In Mathematica, I can simply write the same, using symbolic Pi, and it works as is:

x = 1.2;  #even if this is symbolic 12/10 it will also work
y = Pi/3;
If[x < y, Print["x<y"], Print["x>=y"]]

I did not have to write  y=N[Pi/3]  where N[] is the equivalent function to Maple's evalf() which converts its argument to real.

So, now in Maple, I find myself writing evalf() around so many things, since I have to anticipate I might need to compare them in some logic later on and I can't keep track which one has some symbolic constant such as Pi in them or not. While in Mathematica I never had to worry about this.

Is there a way to reduce the need to having to use evalf() so much?
It seems to me, Maple should be able to decide if  1<Pi without me having to write 1<evalf(Pi) ?