It looks already separable to me. Just treat as a variable so that:
Separating I get:
Integrate, isolate then integrate again.
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
Sorry the initial equation is :
It was probably hard to read before
The problem says to first multiply by a integrating factor
So I get to:
I am then told to make the substitution solve this to show that
f in all of this is a function of n, and the boundary conditions are:
, and approaches 1 as n approaches infinity
Please someone help