Initially I have a function like this:

f''' + 1 - (f')^2 = 0 ... and f' (is f prime)

To solve this I am told to multiply by an integrating factor f'' and then integrate. So I get:

1/2(f'')^2 + f' - 1/3(f')^3 = C

And then the problem says to make a substitution that G = f' so I get:

1/2(G')^2 + G - 1/3(G)^3 = C ...which is a a 1st order ODE but I don't know how to solve that. Can anyone help me?

Thanks