# Math Help - nonlinear ODE

1. ## nonlinear ODE

I must explicitly solve the following ODE

$rf''(r)+f'(r)+f'(r)^3=0$.

I used partial fractions to obtain the equation

$\ln f'(r)+\frac{1}{f'(r)}-\ln(f'(r)+1)=\ln r+k$

for some constant $k$. However, I'm not sure this helps. Any hints or direction would be much appreciated. Thanks!

2. ## Re: nonlinear ODE

I am not sure that your equation is correct :

3. ## Re: nonlinear ODE

You're right... I made an algebra mistake when taking partial fractions. Thanks for the catch!