# First Order Differential Equations

1. Jan 19, 2008

### mit_hacker

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

Solve the following differential equation:

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

2. Relevant equations

3. 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.

2. Jan 19, 2008

### 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 $$y(x)^2=z(x)$$