# Solving two equations with ODE45

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Sergio Manzetti on 4 Apr 2018
Edited: Sergio Manzetti on 4 Apr 2018
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!

Torsten on 4 Apr 2018
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 on 4 Apr 2018
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.

KSSV on 4 Apr 2018
Sergio Manzetti on 4 Apr 2018
That was greek to me. Sorry