# Solve the ODE

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!