Question

The solution of differential equation $\frac{d y}{d x}=\frac{x(2 \ell \ln x+1)}{\sin y+y \cos y}$ is -

• A. $y \sin y=x \ln x+c$
• B. $ y \sin y=x^2 \ln x+c$
• C. $\sin y=x^2 \ell n x+c$
• D. y $\cos y=x^2 \ln x+c$

Answer 1

Answer: (B)

$\frac{d y}{d x}=\frac{x(2 \ell n x+1)}{\sin y+y \cos y}$
$\int(\sin y+y \cos y) d y=\int(2 x \ell n x+x) d x$
using by parts
$y \sin y=x^2 \ell n x+C$