- #1

fluidistic

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## Homework Statement

Solve the following DE: [itex]2xyy'=4x^2+3y^2[/itex].

## Homework Equations

Bernoulli's DE: [itex]y'+P(x)y=Q(x)y^2[/itex].

## The Attempt at a Solution

I know that the original DE isn't under Bernoulli's form, but I have thought a lot on the problem and my feeling is that if I could find a change of variable to transform the general DE into a Bernoulli's equation, I'd be done. I have tried [itex]z=4x^2+3y^2[/itex], so [itex]z'=8x+6yy'[/itex] but this leads me nowhere. I am not even sure I can reduce the original DE into a Bernoulli's equation. This is the only way I think I could solve the DE, I don't see any other way.

I'd love some help.