Solving a Third Order ODE

The equation I have to solve looks something like this:

f'''=1+(f'f''+ff'-f''-f'f''-f'')/f

With Boundary Conditions: f(0)=0, f(1)=1, f'(0)=0, where the equation has been scaled so that 1 is the maximum possible number for f(1)=1.

There are some random constants in there too but those aren't important. The issue I am running into is that at 0, there is a divide by zero that seems to mess up my code. I have tried to get around it by making it a small number that is close but not exactly zero, like .0001, but it still doesn't work. I had been using a Runge Kutta method but my solution kept shooting off to infinity and then to NaN within one iteration. I have been told the finite difference method would be a good thing to try next.

Really, I don't know how to go about solving this equation in MATLAB and I was hoping someone would have a suggestion or a solver or some advice for finite difference or something that would help me out.

Thanks!