Question

If $xdy=y(dx+ydy),y(1)=1$ and $y\left(x_0\right)=-3$, then $x_0=$

• A. $\frac{1}{4}$
• B. $-15$
• C. $-\frac{1}{2}$
• D. $\sqrt{3}e$

Answer 1

Answer: (B)

$xdy=ydx+y^{2}dy\Rightarrow \frac{xdy-ydx}{y^2}=dy$
$\Rightarrow -d\left(\frac{x}{y}\right)=dy$
$-\frac{x}{y}=y+c$ put $x=1y=1\Rightarrow c=-2$
$-\frac{x}{y}=y-2$ put $y=-3$
$\therefore \frac{x}{3}=-5\Rightarrow x=-15$