Question

Solve: $ydx-xdy=xydx$.

Answer 1

Given,

$ydx-xdy=xydx$

$\frac{dx}{x}-\frac{dy}{y}=dx$

integrating on both sides, we get,

$\log x-\log y=x+\log c$

$\log x-\log y=\log e^x+\log c$

$\log \left(\frac{x}{y}\right)=\log \left(c{e}^x\right)$

$\therefore \frac{x}{y}=c{e}^x$