The strategy to find a solution to a homogenous differential equation is to make a substitution that results in a separable equation. For a homogenous equation, either of the substitutions

u $=$

yx

or

v $=$

xy

$.$

will make this work.

Let

u $=$

yx

$,$

or

y $=$ ux$.$

Then

dy $=$ u dx $+$ x du

by the product rule. Use this substitution to simplify the given equation.