# 3rd order nonlinear ODE

1. Apr 21, 2004

### Max0526

Hi, everybody.
I have an ODE:
$$y'''+2y''y-3y'^2=0$$
I know that it has an analytic solution, but I cannot get it (yet).
Can anybody help me?
(I don't need a full explanation how to solve it, just some hints or just the solution with 3 arbitrary constants).
Thanks beforehand,
Max.

2. Aug 25, 2009

### Reb

Three constants? That would be the case if the ODE was linear.

There is another problem here. The ODE is autonomous, and all functions of the form y=const. are solutions, plus the solutions cannot meet each other. So this ODE has only trivial solutions.

3. Aug 25, 2009

### g_edgar

$$y = \frac{6}{x+a}$$

4. Aug 25, 2009