Q. Solution of $\frac{dy}{dx} = \frac{x\log x^{2} + x}{\sin y + y\cos y}$ is
A) $y\sin y = x^{2}\log x + c$
B) $y\sin y = x^{2} + c$
C) $y\sin y = x^{2} + \log x$
D) $y\sin y = x\log x + c$
Explanation
(a)
Given, $\frac{dy}{dx} = \frac{x\log{x^{2} + x}}{\sin y + y\cos y}$
$\Rightarrow$ $\left( \sin y + y\cos y \right)dy = \left( x\log{x^{2} + x} \right)dx$
$\left( \frac{d}{dy}y\sin y \right)dy = \left( \frac{d}{dx}x^{2}\log x \right)dx$
$\Rightarrow$ $y\sin y = x^{2}\log x + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.