Question

Differential equations help

Answer 1

\[\LARGE p^3-2xyp+4y^2=0\]
where p=dy/dx

Answer 2

have to find the solution^

Answer 3

\[\Large (\frac{dy}{dx})^3-2xy \frac{dy}{dx} + 4y^2=0\]

Answer 4

An observation: \[\Large (xy^2)'=y^2+2xyy'\] I don't know how helpful that is, just an idea.

Answer 5

You have a depressed cubic in \(p\), so you might try this method to solve for \(y'\): http://www.sosmath.com/algebra/factor/fac11/fac11.html

I doubt that will give a nice result though