Question

The solution of differential equation $ydx+(2\sqrt{xy}-x)dy=0$ is

• A. $cy=e^{\sqrt{\frac{x}{y}}}$
• B. $cy=e^{-\sqrt{\frac{x}{y}}}$
• C. $cy=e^{\frac{x}{y}}$
• D. $cy=e^{\sqrt{\frac{2x}{y}}}$

Answer 1

The correct option is B $cy=e^{-\sqrt{\frac{x}{y}}}$

$ydx-xdy+2\sqrt{xy}dy=0$
Divide by $y^2$
$\frac{ydx-xdy}{y^2}+2\sqrt{\frac{xy}{y^2}}\frac{dy}{y}=0$
$\frac{d\left(\frac{x}{y}\right)}{\sqrt{\frac{x}{y}}}+2\frac{dy}{y}=0$
$2\sqrt{\frac{x}{y}}+2ln\left(y\right)+2lnc=0$
$cy=e^{-\sqrt{\frac{x}{y}}}$