# 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

### Reb

I mistakingly assumed that every solution has to meet the y axis.

5. Sep 10, 2009

### kosovtsov

You are right, this ODE has an analytic general solution, but it is not so simple and includes hypergeom functions and so on. To see the solution in implicit form use Maple with

ode:=diff(y(x),x,x,x)+2*diff(y(x),x,x)*y(x)-3*diff(y(x),x)^2=0;

ans:=dsolve(ode);