Solving Non-Linear Differential Equation with Fourier Transforms

[Gengar]

Hiya. I have to solve this bad boy under the assumptions that f, f' and f'' tend to 0 as |x| tends to infinity:

1/2(f')^2 = f^3 + (c/2)f^2 + af + b

where a,b,c are constants. My thoughts are use Fourier Transforms to use the assumptions given, but not sure how to do them on these terms. Thanks!

 

[JJacquelin]

Hi !

This is a separable ODE which (in theory) can be solved by direct integration :
df / sqrt(2 f^3 + c f^2 + 2af + 2b) = dx
But the integral involves very complicated elliptic functions, so that it will be of no use in practice.
In particular cases, i.e. for some particular values of a, b, c, it might reduce to simpler functions.