## Using the Poincare-Dulac Thm to develop an iterati...

proc:=changecoords([x,y],logrithmic);
dsolvediff(x,t):=Matrix([[ 1 , 0],
[ 0 , i ]])x+Vector[column]([ x^i ,
0]);
x:=y+h(y);
for i from 2 to 10;
solve;
end do;

endproc;

MakeIteration := proc( expr::algebraic, x::name )
local iteration := diff(x,t)=Matrix([[ 1 , 0 ],
[ 0 , i]])x+Vector[column]([ x^i ,
0]),x:=y+h(y);
for i from 2 to 10 ;
end do ;
unapply(iteration, x);
endproc;
Error, missing operator or ;

Hi , I would like to solve nonlinear equation by using maple,but I wander how I can write it since there is a change of veriable bysubstiuting the value of y in the diifferenitat . Iactually coudnot write the equation sine it contains differential ,matrix and vector . do Ihave to use dalembertian?

best regards

## How to solve symbolically for like following coupl...

I wonder how to solve symbolically for like following coupled ODEs in Maple?

On the other hand, I want to write the code for step by step solution of this problem. But I didn't find algorithm of the solution on the some books. Do you know some books including solving coupled ODEs ?

## struggling to use DEplot with a system of 4 differ...

Ive been trying to plot the following system

With these initial conditions (Also G*M=1)

ics:=[x(0)=1, y(0)=0,vx(0)=0,vy(0)=1];

I use this command to try and do this

with(DEtools):
DEplot(subs({G=1,M=1},satODE1),{x(t),y(t),vx(t),vy(t)},t=-2..2,ics,scene=[x(t),y(t)],scaling=constrained);

But I get this error message

Error, (in DEtools/DEplot/CheckInitial) too few initial conditions: [x(0) = 1]

Which I find odd because I have an initial condition for each variable

Im not sure what makes this different to other DE's Ive plotted other than having more equations in the system

## Why Maple does not solve this simple system of dif...

Hi,

Can somebody help me to find out why Maple can't completely solve this system of differential equations?

The answer to the previous command is

but I don't get the solution for u(x). This should be u(x)=-x+x^2/2.

## How do I solve a partial differential equation wit...

Hi all,

I have a partial differential equation similar to the following:

Equation: f_x(x,y) + f_y(x,y) = f(x,y) + f(x,0),
Boundary value conditions: f(x,10) = f(10,y) = 0.

The solution is that f is identically equal to 0.

However, I am having trouble solving this equation in Maple. I type the following:

pde := diff(f(x, y), x)+diff(f(x, y), y) = f(x, y)+f(x, 0);

bv1 := f(x, 10) = 0;

bv2 := f(10, y) = 0;

solution := pdsolve(pde, {bv1, bv2}, numeric, time = x, range = 0 .. 10);

When Maple tries to evaluate the last expression, I get the error

Error, (in pdsolve/numeric/process_PDEs) PDEs can only contain dependent variables with direct dependence on the independent variables of the problem, got {f(x, 0)}

It seems to have difficulties with the expression "f(x,0)". Is there some trick to typing this in a way that makes Maple interpret it correctly?

Edit: I encounter the same problem, when I try to solve the ODE f'(x) = f(x) + f(0), where f(10) = 0.

Best regards.

## How can I solve Linear ODEs system using matrix me...

$$\textbf{x}' = \begin{bmatrix} -4 & -2 \\ 3 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}+\begin{bmatrix} -t \\ -2t-1 \end{bmatrix},\textbf{x}(0)=\begin{bmatrix} 3 \\ -5 \end{bmatrix}$$

As I know firstly, when the matrix is denoted by $A$, we must compute $e^{At}$ by diagonalizing $A$: if $A=PDP^{-1}$ for a diagonal $D$ then $e^{At} = P e^{Dt} P^{-1}$ where $e^{Dt}$ is a diagonal matrix with $(e^{Dt})_{ii} = e^{D_{ii} t}$...

How can I write The Maple code? maple.stackexchange)

restart: with(LinearAlgebra):

A := Matrix(2,2,[-4,-2,3,1]);

....

## How do I solve the two dimensional P.D.E in Maple?...

i have an example, u[t] = u[xx]^2+u[yy]^2+u[zz]^2 with subject to b.c. u[0](x,y,z,t):=2*sin(x)*sin(y)*sin(z)
i used adomian method to solve this P.D.E, but i failed to construct a code of 2D P.D.E.
kindly help me in this regard

## how i can pdsolve this nonlinear equations...

thanksoffcenter2.mw

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#####################################

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at x=

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############################################

at x=0

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################################################

at t=0 for x= [0,La]

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######################################################

at t=0 for x= [0,La)

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###################################################

at t=0 for x=La

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## Replacing variable in ODE...

Hi,

It might be very silly question, but i dont know why it is not working out. So here is the question. In the attached maple shhet when i am trying to substitute eta(t)=epsilon*z(t) then it is not making that susbtitution for differential operator. Apart from that when i m collecting epsilon terms then also it not collecting it.quesiton.mw

Regards

Sunit

## Bifurcation plot for ODE system with delay...

Consider the following dynamical systems with time delay:

diff(x(t), t) = y(t)-bx(t)^3+ax(t)^2-z(t-tau)+I

diff(y(t), t) = c-dx(t)^2-y(t)

diff(z(t), t) = r(s(x-beta)-z(t))

Here the values of the parameters are a = 3, b = 1, c = 1, d = 5, s = 4, beta = 1.6, r = 0.6e-2, I = 3.0

How to write code for bifurcation plot for the above differential equations with delay.

Delay as taken as bifurcation parameter.

## Solution of PDE...

i want to solve these two coupled eqaut with finite boundary conditionsions. Can some one help me

eq1:=diff(f(eta),eta,eta,eta,eta)+2*(epsilon/(1+epsilon*theta(eta)))^2*diff(f(eta),eta,eta)*((diff(theta(eta),eta))^2)-(epsilon/(1+epsilon*theta(eta)))*(diff(theta(eta),eta,eta))*(diff(f(eta),eta,eta))=0;

eq2:=diff(theta(eta),eta,eta)+Pr*Re*f(eta)*diff(theta(eta),eta)=0;

Re:=1:Pr:=1:epsilon:=0.25:

bc:=f(1)=0,D(f)(-1)=0,D(f)(1)=1,D(f)(-1)=1,theta(-1)=0,theta(1)=0;

## Falkner-Skan equation...

Hi,

I want to solve the Falkner-Skan equation numbercally using maple. The Falkner-Skan equation is

f′′′ + ff′′ + (1 − (f′)^2)=0 ,

with subject to the boundary conditions,

f(0) =0 ; f′(0) = 0,

f′(∞) = 1.

And then save the data in DATfile in order to plot using Gnuplot?

Regards

## Logplot of ODE solution...

I have some differential equations that I want to plot on the same axis (as i have below), but would like to plot with a log scale to illustrate the fact that one is simply a logarithmic decay (solid line) and all the others are not.

I had used deplot and display to make the above graph,

but if you want more detail, here is a worksheet with the relevant differntial equations:

## Change PDE into ODE...

PLEASE..!! CAN ANYONE HELP ME IN CODING ON MAPPLE 13 TO CHANGE PDE INTO ODE??

MY FUNCTION IS THIS

U[t, t]-U[t, t, x, x]-(aU[]-b*U[]^3)[x, x] = 0

## Why are different answers produced?...

PrimesQuestion.mw

Please let me know if this link correctly accesses my worksheet. If not, I will copy its contents into this question.

Which ODE in the worksheet, if any, provides the correct answer?

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