Solve y' = (y/x) + (2x³cos(x²)/y)

[mit_hacker]

Homework Statement

Solve the following differential equation:

y' = (y/x) + (2x^3Cos(x^2)/y).

Homework Equations

The Attempt at a Solution

You certainly can't separate variables here and you can't put it in the form in which you can find the integrating factor. This is not a Bernoulli equation and neither can it be solved by the y/x = z substitution. I am completely stumped! Please help.

 

[Rainbow Child]

This is a non-linear ODE. To make it linear multiply by $$y(x)$$ and observe that

$$y'(x)\,y(x)=\frac{1}{2}\,(y(x)^2)'$$

and try then the substitution $$y(x)^2=z(x)$$