Question

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

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

Answer 1

Answer: (B)

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