Question

The solution of the differential equation $\frac{d y}{d x}$ = $\frac{y c o s \, x - y^{2}}{sin x}$ is equal to (where $c$ is an arbitrary constant)

• A. $sin x=x-y+c$
• B. $sin x=x+y+c$
• C. $sin x=xy+cy$
• D. $\frac{sin x}{x}=y+c$

Answer 1

Answer: (C)

$\frac{d y}{d x}=\frac{y c o s x - y^{2}}{sin x}$
$ycos xdx-sin⁡xdy=y^{2}dx$
$\frac{y c o s x . d x - sin x . d y}{y^{2}}=dx$
$d\left(\frac{sin x}{y}\right)=dx$
On integrating, we get,
$\frac{sin x}{y}=x+c$
$sin x=xy+cy$