The usual procedure is to let and Then your DE would translate to the following system:
Question: are the conditions accurate? Because those are mixed boundary conditions, not initial conditions. That will radically change the method of solution. I would probably do some sort of shooting method (pick initial conditions, and try to "hit" the end conditions - keep doing until you get close enough).
If those conditions are accurate, you could try a combination of Runge-Kutta 4 with a shooting method.