- #1

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## Homework Statement

[itex]y' = \frac{2xy + y^{2} + 1}{y(2+3y)}[/itex]

## Homework Equations

## The Attempt at a Solution

First I tried making a substitution in the case that it is homogeneous, but it didn't make the equation separable. It's not linear, it's not exact, and not separable.

Does it become exact when multiplying by some function?

I just need a little guidance for what method I should use to solve.

After making a substitution y = vx,

[itex]v + xv' = \frac{2x^{2}v + v^{2}x^{2} + 1}{vx(2+3vx)}[/itex]

This doesn't seem to simplify into anything separablem, after doing some algebra. Any ideas?