Solve ODE with BC

Hi, I would like to solve this ODE with initial conditions y=0 and y'=0, and boundary cond L=[0,1] using the given command:

 syms x y(x) 
 % Define first and second derivatives for y
 Dy   = diff(y,x);
  % Define differential equation
 Diff = (1i*diff(y,x)-x)^2+x^2 == 0.326307*y;
 % Set initial conditions
 y     = y(0)    == 0;
 Dy    = diff(y,0) == 0;
 % Solve differential equation and display
 Uc_sym  = dsolve(Diff, y, Dy);
 display(['y = ',char(10),char(Uc_sym),char(10)])
Alternatively, check out this example in the documentation.

But I am not aware on how to include the BCs and how to make this script work at all.. Can someone help?

Thanks

Answer 1

[Stephan]

I doubt that your ode has an analytical solution - however here is a minimal working example of how to include BC's in a symbolic way:

 syms y(x)
 
 % Define first derivative for y
 Dy = diff(y,x);
 
 % Define differential equation
 ode = y == Dy * x;
  
 % Set conditions
 conds = [y(0)==0, y(1)==2, Dy(0)==2, Dy(1)==2];
 
 % Solve differential equation and display
 sol = dsolve(ode, conds)

If you dont find an analytical solution use bvp4c instead to solve numeric.

[Sergio Manzetti]

Thanks! Seems solving this problem with bvp4c is not easy at all, although the problem here and the BC conditions are quite straight forward presented.