2\sqrt{xy}dy+ydx-xdy=0
Dividing the diff equation by x1/2y3/2
2\frac{dy}{y}+\sqrt{\frac{y}{x}}\left( \frac{ydx-xdy}{y^{2}}\right)=0
2\frac{dy}{y}+\frac{d(x/y)}{\sqrt{x/y}}=0
lny+\sqrt{\frac{x}{y}}=c
2\sqrt{xy}dy+ydx-xdy=0
Dividing the diff equation by x1/2y3/2
2\frac{dy}{y}+\sqrt{\frac{y}{x}}\left( \frac{ydx-xdy}{y^{2}}\right)=0
2\frac{dy}{y}+\frac{d(x/y)}{\sqrt{x/y}}=0
lny+\sqrt{\frac{x}{y}}=c