# Nonlinear ODE

1. Nov 18, 2008

### John Sebastia

I was looking for some guidance on how to attack this problem.

Consider the nonlinear ODE:

y'(x)+y$$^{}2$$(x)+Ay(x)+B=0

(y prime + y squared with A and B constant coefficients)

Show that the solution is given by y=z'/z, where z(x) solves the second order ODE:

z''+Az'+Bz=0

(z double prime plus z prime with A and B constant coefficients)

Any advice would be greatly appreciated!

Thanks!!

2. Nov 18, 2008

### tiny-tim

Welcome to PF!

Hi John! Welcome to PF!

If y = z'/z, then y' = … ?

Now subsitute into the original equation, and multiply by z.

3. Nov 18, 2008

### John Sebastia

Really. Is that all that needs to be done? I did that and got the original equation to look like the second one. So then that makes it a solution for the first equation right? Hmm, I guess that was easy. Thanks!