If \(\displaystyle \frac{dy}{dx}= \frac{cx}{y}\) then \(\displaystyle ydy= cxdx\) so, integrating, \(\displaystyle \frac{cx^2}{2}= \frac{y^2}{2}+ C\) which is the same as \(\displaystyle \frac{cx^2}{2}- \frac{y^2}{2}= C\), a family of hyperbolas all having (0, 0) as center and \(\displaystyle cx^2- y^2=(\sqrt{c}x- y)(\sqrt{c}x+ y)= 0\) as asymptotes.