Q. The solution of the differential equation $\frac{dy}{dx} = x\log x$ is
A) $y = x^{2}\log x - \frac{x^{2}}{2} + c$
B) $y = \frac{x^{2}}{2}\log x - \frac{x^{2}}{4} + c$
C) $y = \frac{x^{2}}{2} + \frac{x^{2}}{2}\log x + c$
D) None of these
Explanation
(b)
Given, $dy = x\log x\ dx$
$\Rightarrow$ $y = \frac{x^{2}}{2}\log x - \int_{}^{}\frac{x}{2}dx$ [integrating]
$\Rightarrow$ $y = \frac{x^{2}}{2}\log x - \frac{x^{2}}{4} + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.