Question

Solve it:-
$xdy+2ydx=0$ when $x=2,y=1$

Answer 1

Solution -

$xdy+2ydx=0$ $y\left(2\right)=1$

$\frac{-dy}{y}=\frac{2dx}{x}$

$-ln\left|y\right|=2ln\left|x\right|+c$

Put $x=2,y=1$

$2ln2+c=0$

$c=-ln4$

$-ln\left|y\right|=2ln\left|x\right|-ln4$

$ln\frac{x^2}{4}+lny=0$

$\frac{x^{2}y}{4}=1$

$y=\frac{4}{x^2}$