- #1
bitrex
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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.