Q. The solution of the differential equation $x\ \frac{dy}{dx} + 2y = x^{2}$ is
A) $y = \frac{x^{2} + c}{4x^{2}}$
B) $y = \frac{x^{2}}{4} + c$
C) $y = \frac{x^{4} + c}{x^{2}}$
D) $y = \frac{x^{4} + c}{4x^{2}}$
Explanation
(d)
Given, $\frac{dy}{dx} + \frac{2}{x}\ y = x$
$\therefore$ Integrating factor =$e^{\int_{}^{}{\frac{2}{x}\ dx}} = x^{2}$
$\therefore$ Required solution is
$y.x^{2} = \int_{}^{}x^{3}\ dx = \frac{x^{4}}{4} + \frac{c}{4}$
$\therefore$ $y = \frac{x^{4} + c}{4x^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.