# Non linear second order diff eq

1. Feb 3, 2009

### rbetzel

I'm trying to find a substitution that works for the nonlin diffeq

y''+a(y')^2-by=0

Any suggestions?

2. Feb 3, 2009

### NoMoreExams

If you differentiate again, you get

$$y^{'''} + 2ay^{'} \cdot y^{''} - b = 0$$ right?

If you let

$$u = y^{'}$$ you get $$u^{''} + 2a u^{'}u - b = 0$$