Shooting method for boundary value problems

I use ODE45 and the shooting method to solve boundary value problems. There was a specific case in second order differential equations, where an unknown initial condition (which is to be found using shooting method) is a part of the expression of the second derivative, something like the following code. I want to know how to include it in the function and do I need to use any looping statements for it.

funtion dy = diffe(x,y)
l = 2;
p = 3;
dy = [y(2); p*x^2+2*y(1)+y0];
end

So in this code, value of dy/dx at x=0 is known but the value of y at x=0 is not known, but the value of y at x=1 (second boundary is known). This function is to be called like this:

funtion odesolver
dy0 = 0;
[x,y] = ode45(@diffe, [0 1], [y0, dy0]);
end

If someone can recommend a solution to this, that'll be very helpful.

[Torsten]

Use BVP4C instead of ODE45.

Answer 1

[Basavaraj]

funtion dy = diffe(x,y)

l = 2;

p = 3;

dy = [y(2); p*x^2+2*y(1)+y0];

end

funtion odesolver

dy0 = 0;

[x,y] = ode45(@diffe, [0 1], [y0, dy0]);

end