Question

Solve :
$\frac{xdx+ydy}{\sqrt{x^2+y^2}}=\frac{xdy-ydx}{x^2}$

Answer 1

Given,

$\frac{xdx+ydy}{\sqrt{x^2+y^2}}=\frac{xdy-ydx}{x^2}$

or, $\frac{1}{2}\frac{d(x^2+y^2)}{\sqrt{x^2+y^2}}=d\left(\frac{y}{x}\right)$

Now integrating both sides we get,

$\sqrt{x^2+y^2}=\frac{y}{x}+c$ [ Where $c$ is integrating constant]