# Homework Help: Non Linear ODE

1. Sep 29, 2010

1. The problem statement, all variables and given/known data

$$\left(\frac{dy}{dx}\right)^2 - 4x\frac{dy}{dx} + 6y = 0$$

2. Relevant equations

A common approach we have used for similar problems has been to let P = dy/dx

3. The attempt at a solution

Doing so we have:

$$P^2 - 4xP +6y = 0$$

$$\Rightarrow 6y = 4P(x - P)$$

Differentiating gives:

$$6P = 4\left[P(1 - \frac{dP}{dx}) +\frac{dP}{dx}(x - P)\right] = 0$$

Now usually we try to factor this and solve each factor as a linear 1st order EQ in P. However, I am having trouble seeing a nice way to factor this, that makes each factor linear. All I can get to is

$$-2\left[P+2\frac{dP}{dx} - 2x\frac{dP}{dx} + 2P\frac{dP}{dx}\right] = 0$$

Any thoughts on what to do with the bracketed term to get 2 linear EQs out of the deal?

Thanks