Question

By inspection find a one-parameter family of solutions of the differential equation xy'=y. verify

Answer 1

Try this:
$\frac{y'}{y} =x; \ =\ \textgreater \ \ \frac{dy}{y}= \frac{dx}{x}; \ =\ \textgreater \ \ lny=lnx+C; \ =\ \textgreater \ \ y=Cx$