Thread: Reducing order of DFQ and solving

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

It looks already separable to me. Just treat as a variable so that:



Separating I get:



Integrate, isolate then integrate again.

Originally Posted by shawsend

It looks already separable to me. Just treat as a variable so that:



Separating I get:



Integrate, isolate then integrate again.

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