Using the substitution $y = vx$, where $v$ is a function of $x$, solve \(x \frac{\mathrm{

Question

Using the substitution $y = vx$, where $v$ is a function of $x$, solve $x \frac{\mathrm{d}y}{\mathrm{d}x} - y = \sqrt{x^2 - y^2}$.

Accepted Answer

$y = x \sin(\ln|x| + C)$.

Solving a homogeneous quation