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## Homework Statement

I have to solve the following differential equation by the "variation of parameters" method.

## Homework Equations

[tex]\frac{dy}{dx}x +2y = 3x[/tex]

## The Attempt at a Solution

The associated homogeneous equation of the initial equation is:

[tex]\frac{dy}{dx} = -2x^{-1}y[/tex]

So

[tex]\frac{1}{y}dy = -2x^{-1}dx[/tex]

[tex]ln(y) = -2ln(x)[/tex]

[tex]ln(y) = ln(x^{-2})[/tex]

[tex]y = x^{-2}[/tex]

Unfortunately, this doesn't satisfy the homogeneous equation.