Discretization of a Third Order ODE for Finite Difference method

The equation I have to solve looks something like this:

f'''=1+f’+(f'f'''-f''-100f'f''-10f'')/f W ith 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.

I'm trying to solve this with a Finite Difference Method, probably the central method, but I'm having trouble discretizing the function into a codable form. I am trying to solve the discretized form with a Gauss-Seidel solution method and for that I need to properly break down this equation into nodes that I can code into the Coefficient matrix for Ax=b.

Any help with coding a finite difference method for this specific ODE would be greatly appreciated!