Question

If $xdy=ydx+y^{2}dy$ and $y(1)=1$ then find the value of $y(-3)$.

Answer 1

Answer: 3.00

$\int \frac{ydx-xdy}{y^2}=\int -dy$
$\frac{x}{y}=-y+c$
As, $y(1)=1$
$1=-1+c$
$\Rightarrow c=2$
$\Rightarrow \frac{x}{y}=-y+2$
If $x=-3$
$-3=-y^2+2y$
$\Rightarrow y^2-2y-3=0$
$\Rightarrow y=3$