- #1

Saladsamurai

- 3,020

- 7

## Homework Statement

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

## Homework Equations

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

## The Attempt at a Solution

Doing so we have:

[tex]P^2 - 4xP +6y = 0[/tex]

[tex]\Rightarrow 6y = 4P(x - P)[/tex]

Differentiating gives:

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

[tex]-2\left[P+2\frac{dP}{dx} - 2x\frac{dP}{dx} + 2P\frac{dP}{dx}\right] = 0[/tex]Any thoughts on what to do with the bracketed term to get 2 linear EQs out of the deal?

Thanks