Question

If $x d y=y(d x+y d y), y(1)=1$ 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)

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