How do I prepare the following ODE for ode45?

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Sergio Manzetti on 20 Feb 2018
Commented: Torsten on 9 Mar 2018
Hello, I would like to solve the following ODE in ode45, but the example's on the site are not describing using higher order derivatives with non-linear terms.
The ODE is:
y''' = y(2+x^2)
initial conditions are: y(0)=0 y'(0)=0 y''(0)=0
Thanks!
Sergio Manzetti on 20 Feb 2018
I got so far:
dYdX = @(X,Y) [Y(3) + (x^2+2)*Y(1)]; % Differential equation
res = @(ya,yb) [ya(1); ya(2); yb(2)-1]; % Boundary conditions
SolYinit = bvpinit([0 1E+1], [1; 1; 1]);
Fsol = bvp4c(dYdX, res, SolYinit);
X = Fsol.x;
F = Fsol.y;
figure(1)
plot(X, F)
legend('F_1', 'F_2', 'F_3', 3)
grid
But the first line is not correct. Can you see what is missing?

Torsten on 20 Feb 2018
fun = @(x,y)[y(2);y(3);y(1)*(2+x^2)];
y0 = [0 0 0];
xspan = [0 5];
[X,Y] = ode45(fun,xspan,y0);
plot(X,Y(:,1),X,Y(:,2),X,Y(:,3));
Best wishes
Torsten.
Torsten on 28 Feb 2018
Maybe, if you tell us what the "square modulus of the numerical solution" is.

Sergio Manzetti on 28 Feb 2018
Edited: Sergio Manzetti on 28 Feb 2018
(abs(y))^2
if y is the solution
Torsten on 9 Mar 2018
You transform a higher order ODE to a system of first-order ODEs.