Ok, thanks!
The solution given is correct but it isn't the only solution. Yes, you'll have to handle the boundary condition at L separately.
So, if I understood Mathematica doesn't solve the equation automatically.
The last boundary condition will have to be me adding it, right?
Replace y[L] ==0 with y'[0] == yp0 and then combine y[L] ==0 with the solution you get.
