## plot an ode and a function in the same plot...

Hi

I have an ODE which is based on a seperate function, and I would like to make a plot with the information

dsolve([diff(X(W), W) = (0.536000000000000e-3*(1-X(W)))*(1+X(W)), X(0) = 0], numeric)

and

C_A:= C_A0*(1-X(W))*(1+X(W))

which has been used as part of the ODE.

I would really like to plot C_A as a function of W. I have no problem plotting X as a function to W using odeplot. Ideally I would like to plot C_A and X vs W in the same plot.

Regards

## How do I solve an ODE with initial value condition...

the question is

ODE5:= y(x)*diff(y(x),x,x) + (diff(y(x),x)^2=0

dsolve({ODE5,y(0)=4,D(y)(0)=7},y(x))

and my answer appears to be an integration! which is wrong

Could someone tell me what did I do wrong? And how could I get to this result?

Thanks a lot!

## Need Help to Plot BVP graph...

Please i need help to plot the graph of f'' against episoln using the below BVP

HELP.mw

## To find the numerical solutions of system of nonli...

Dears

Hope everything fine with you. I want to solve the attached problem by numarically and want to plot it but failed. Please see the attachement and correct it. I am waiting your positive respone.

System_of_ODEs.mw

With my best regards and sincerely.

School of Mathematical Sciences
Peking University, Beijing, China

## how can i solve the following odes...

i don't know much about maple, i need to solve the following odes system... I study a little on the help page of maple about numeric[midrich] that takes bvp and deal singularity as well but dint know how to used in the following system

odes.mw

## ODE with boundary conditions involving limits...

Respected member!
Please help me to find the solution of attached problem, I am a new user so pleaes forgive any mistakes.

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## how to solve the challenging non linear coupled 1s...

G := 6.6743*10^(-8);

a := 1.9501*10^24;

b := .3306;

c := 2.99792458*10^10;

d := 2.035;

pi := 3.143;

eps := 3.8220*10^35;

g(r) = 1-s(r)/0.06123;

j(r) = e^(-(1/2)*w(r))*(1-2*G*v(r)/(r*c^2))^.5

sys := diff(v(r), r) = 4*pi*r^2*eps/c^2, ics=v(0)=0

diff(u(r), r) = -G*(eps+u(r))*(v(r)+4*Pi*r^3*u(r)/c^2)/(c^2*(r^2-2*G*r*v(r)/c^2)),u(0)=1.3668*10^34

diff(w(r), r) = 1.485232054*10^(-28)*(v(r)+4.450600224*10^(-21)*pi*r^3*u(r))/(r^2-2*G*r*v(r)/c^2), conditions: w(0)=0,iterate it to find w(688240)=-2.05684, it solve must satistfy the both conditions.

diff(r^4*j(r)*(diff(g(r), r)), r)+4*r^3*g(r)*(diff(j(r), r)) = 0, conditions dg(r)/dr =0  at r=0, g(688240) =0.87214

diff(J(r), r) = (8*pi*(1/3))*(eps/c^2+u(r)/c^2)*(g(r)*j(r).(r^4))/(1-2*G*v(r)/(r*c^2)) condition J(0)=0.

## 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]);

....

## boundary conditions...

Dear sir in this problem should accept five boundaryconditions but it is not working for five boundary conditions and showing the following error please can you tell why it is like this ??

Error, (in dsolve/numeric/bvp/convertsys) too many boundary conditions: expected 4, got 5
Error, (in plots:-display) expecting plot structures but received: [fplt[1], fplt[2], fplt[3], fplt[4], fplt[5], fplt[6], fplt[7]]
Error, (in plots:-display) expecting plot structures but received: [tplt[1], tplt[2], tplt[3], tplt[4], tplt[5], tplt[6], tplt[7]]

stretching_cylinder_new1.mw

## Does TWS command of Maple solves system of ODEs ?...

Dear all

I am trying to solve system of ODEs by TWS command for traveling wave solution, but an error is showing. When I enter sinlge ODE or PDE the command does not show any error. Why it is showing error for system of ODEs ?

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## Method for numerical solving BVP of ODE with disco...

I try to solve numerically a boundary VP for ODE with different order of discontinuity of right part.

Say, the following BVP is given:

y''(x)+y'(x)+y(x)=F(x)

y(0)=1, y(2)=1

Let's use piecewise right part

F  := piecewise(x<=1, -x, x>1, 2*x+(x-1)^2)

The function

piecewise(x<=1, 1-x, x>1, (x-1)^2)

as obviuos, satisfies the BVP exclung the point x=1, where its 1st and 2nd derivatives are discontinuos.

Numerical solution

N0:=6:
As:=dsolve([diff(y(x), x$2)+diff(y(x), x)+y(x)=F, y(0)=1, y(2)=1], y(x), type=numeric, output = Array([seq(2.0*k/N0, k=0..N0)]), 'maxmesh'=500, 'abserr'=1e-3): provides the solution essentially different to exact one described above: But if to use the right part F := piecewise(x<=1, x^2+x+2, x>1, -x^2+x) for which the function piecewise(x<=1, 1-x+x^2, x>1, -1+3*x-x^2) satisfies the BVP excluding x=1, where this function has discontinuity of 2nd derivative only, the corresponding numerical solution is very similar to this exact solution: This reason of the difference between these two cases is clear. In the first case both 1st and 2nd derivatives are discontiuos, while in the second one -- 1st derivative is contiuos. I wonder, if there are numerical methods, implemeted in Maple, for numerical solution of the first type BVP with non-smooth right part? ## Library, Shooting, ode... Asked by: what does it means and what it will do. Can some one help me for solving this Shootlib := "C:/Shoot9"; libname := Shootlib, libname; with(Shoot); while i m receiving the following message: "Error, invalid input: with expects its 1st argument, pname, to be of type {module, package}, but received Shoot " Full program is : restart; Shootlib := "C:/Shoot9"; libname := Shootlib, libname; with(Shoot); with(plots): N1 := 1.0; N2 := 2.0; N3 := .5; Bt := 6; Re_m := N1*Bt; gamma1 := 1; FNS := {f(eta), fp(eta), fpp(eta), g(eta), gp(eta), m(eta), mp(eta), n(eta), np(eta), fppp(eta)}; ODE := {diff(f(eta), eta) = fp(eta), diff(fp(eta), eta) = fpp(eta), diff(fpp(eta), eta) = fppp(eta), diff(g(eta), eta) = gp(eta), diff(gp(eta), eta) = N1*(2.*g(eta)+(eta-2.*f(eta))*gp(eta)+2.*g(eta)*fp(eta)+2.*N2*N3*(m(eta)*np(eta)-n(eta)*mp(eta))), diff(m(eta), eta) = mp(eta), diff(mp(eta), eta) = Re_m*(m(eta)+(eta-2.*f(eta))*mp(eta)+2.*m(eta)*fp(eta)), diff(n(eta), eta) = np(eta), diff(np(eta), eta) = Re_m*(2.*n(eta)+(eta-2.*f(eta))*np(eta)+2.*N2/N3*m(eta)*gp(eta)), diff(fppp(eta), eta) = N1*(3.*fpp(eta)+(eta-2.*f(eta))*fppp(eta)-2.*N2*N2*m(eta)*(diff(mp(eta), eta))) }: blt := 1.0; IC := { f(0) = 0, fp(0) = 0, fpp(0) = alpha1, g(0) = 1, gp(0) = beta1, m(0) = 0, mp(0) = beta2, n(0) = 0, np(0) = beta3, fppp(0) = alpha2 }; BC := { f(blt) = .5, fp(blt) = 0, g(blt) = 0, m(blt) = 1, n(blt) = 1}; infolevel[shoot] := 1; ## Plotting ode solutions... Asked by: Hi, I'm being unable to plot the solution to the equation schro := {-(diff(psi(x), x, x))+(2*a*b*x^4+a^2*x^6+(b^2-a*(2*p+3))*x^2-(2*p+1)*b)*psi(x) = 0}; for the special cases of a=b=1 and p=0 and p=1 I've used dsolve and am getting Heun functions :-( The claim is that the solutions come out to be exponentials of the form: psi(x)=(x^p)*exp(-(a*(x^4))/4 - (b*(x^2))/2) thanks in advance ## Solution to BVP , pls help... Asked by: Am trying to valid a research work done by kuiken(1968) Kuiken_(1968).pdf where we have this two eauations: restart; Digits := 35; with(ODETools); with(student); with(plots); inf := 4; equ1 := diff(f[0](eta), $(eta, 3))+theta[0](eta);
equ2 := diff(theta[0](eta), \$(eta, 2))+3*f[0](eta)*(diff(theta[0](eta), eta));
Bcs1 := f[0](0) = 0, (D(f[0]))(0) = 0, theta[0](0) = 1, theta[0](inf) = 0, (D(D(f[0])))(inf) = 0;
S1 := dsolve({Bcs1, equ1, equ2}, {f[0](eta), theta[0](eta)}, type = numeric, method = bvp[midrich]);
proc(x_bvp)  ...  end;
S1(0);
[                            d
[eta = 0., f[0](eta) = 0., ----- f[0](eta) = 0.,
[                           deta

d   /  d            \
----- |----- f[0](eta)| = 0.82449782146165697398999365896678734,
deta \ deta          /

theta[0](eta) = 1.0000000000000000000000000000000000,

d                                                         ]
----- theta[0](eta) = -0.71098574970825563256340736114251047]
deta                                                       ]
S1(inf);
[
[eta = 4., f[0](eta) = 1.7815670728545914261072119522795076,
[

d
----- f[0](eta) = 0.51061876174095320088291844433043562,
deta

d   /  d            \
----- |----- f[0](eta)| = 0., theta[0](eta) = 0.,
deta \ deta          /

d
----- theta[0](eta) = -0.000054818176138173095945902421930470836
deta

]
]
]

Pls, I need to find the function of the limit of f[0](eta) at eta tend to infinity. checked equation 45 of the attached document and for the two equation pls checked equation 36 and 37 for the ODE equation solved above.

Kuiken_solution for equation 36 and 37.pdf

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