Solving two equations with ODE45

Hi, I used the following command to solve one ODE

fun = @(x,y)[y(2);y(3);(y(1)*(1-x^2))];
y0 = [1 0 8]; %y, y', y''
xspan = [-3 3];
[X,Y] = ode45(fun,xspan,y0);
plot(X,Y(:,1)),,% X,Y(:,2),X,Y(:,3),X,Y(:,1).* (2 + X .^ 2));

However, I would like to solve this pair of equations instead of the given "fun":

How do I add two equations in the fun line?

Thanks!

Answer 1

[Torsten]

fun=@(x,y)[y(2);y(3);-(1+x^2)*y(4);y(5);y(6);(1+x^2)*y(1)]; %psi2,psi2',psi2'',psi1,psi1',psi1''

Best wishes

Torsten.

[Sergio Manzetti]

Thanks Torsten! I want to make sure you saw the right equation, it is only composed of third order derivative!

[Sergio Manzetti]

I get an error:

Index exceeds matrix dimensions.

Error in Schroding_plot>@(x,y)[y(2);y(3);-(1+x^2)*y(4);y(5);y(6);(1+x^2)*y(1)]

Error in odearguments (line 90)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.

Error in ode45 (line 115)
    odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in Plot (line 8)
[X,Y] = ode45(fun,xspan,y0);

with

fun=@(x,y)[y(2);y(3);-(1+x^2)*y(4);y(5);y(6);(1+x^2)*y(1)]; %psi2,psi2',psi2'',psi1,psi1',psi1''
y0 = [1 0 8]; %y, y', y''
xspan = [-3 3];
[X,Y] = ode45(fun,xspan,y0);
plot(X,Y(:,1)), X,Y(:,2),X,Y(:,3),X,Y(:,1).* (2 + X .^ 2);

[Torsten]

You must change y0 to a 6x1 column vector.

And I saw the equations for psi1 and psi2.

[Sergio Manzetti]

How would that look like in the plot part?

I wrote now:

plot(X,Y(:,1)), X,Y(:,2),X,Y(:,3),X,Y(:,1);
plot(X,Y(:,2)), X,Y(:,2),X,Y(:,3),X,Y(:,1);

both should have the same start conditions, but I am not sure here how to distinguish y_1 and y_2 in the plot

[Torsten]

The examples under

https://de.mathworks.com/help/matlab/ref/ode45.html

help you to distinguish between plot curves.

Best wishes

Torsten.

[Sergio Manzetti]

Ok, now its more clear with your link:

I used this :

fun=@(x,y)[y(2);y(3);-(1+x^2)*y(4);y(5);(1+x^2)*y(1)]; %psi2,psi2',psi2'',psi1,psi1',psi1''
y0 = [1 0 8]; %y, y', y''
xspan = [-3 3];
[X,Y] = ode45(fun,xspan,y0);
plot(X,Y(:,1)), X,Y(:,2),X,Y(:,3),X,Y(:,1), '-o',X,Y(:,2), X,Y(:,2),X,Y(:,3),X,Y(:,1);

but then I got that again :

Index exceeds matrix dimensions.

Error in plot>@(x,y)[y(2);y(3);-(1+x^2)*y(4);y(5);(1+x^2)*y(1)]

Error in odearguments (line 90)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.

Error in ode45 (line 115)
    odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in plot (line 8)
[X,Y] = ode45(fun,xspan,y0);

isn't the use of the '-o' what I needed here?

[Torsten]

fun is incorrect (5 instead of 6 components), y0 is inconsistent (3 instead of 6 initial values), plot(X,Y(:,1)),X,... doesn't make sense.

[Sergio Manzetti]

Thanks, following your link I used a new y0 and got a result, but plot only plots one form.

fun=@(x,y)[y(2);y(3);-(1+x^2)*y(4);y(5);y(6);(1+x^2)*y(1)]; %psi2,psi2',psi2'',psi1,psi1',psi1''
y0 = [1 0 8 1 0 8]; %y, y', y''
xspan = [-3 3];
[X,Y] = ode45(fun,xspan,y0);
 plot(X,Y(:,1)), X,Y(:,2),X,Y(:,3),X,Y(:,1), '-o',X,Y(:,2), X,Y(:,2),X,Y(:,3),X,Y(:,1);

What is wrong in the plot section really?

[Sergio Manzetti]

Hi Torsten, I edited this finally:

    fun=@(x,y)[y(2);y(3);-(1+x^2)*y(4);y(5);y(6);(1+x^2)*y(1)]; %psi2,psi2',psi2'',psi1,psi1',psi1''
    y0 = [1 0 8 1 0 8]; %y, y', y''
    xspan = [-3 3];
    [X,Y] = ode45(fun,xspan,y0);
  plot(X,Y(:,1)), X,Y(:,2),X,Y(:,3),X,Y(:,1);

So it shows a plot. But this plot is identical to the plot of only one function present in the command (remove the second function and decrease to three dimensions, and it is the same plot).

Is that correct? I would have expected a different solution.

Answer 2

[KSSV]

This could help you: https://in.mathworks.com/matlabcentral/fileexchange/33168-springpendulum

[Sergio Manzetti]

That was greek to me. Sorry