Q. Solution of the differential equation $\frac{dy}{dx} + \frac{y}{x} = \sin x$ is
A) $x\left( y + \cos x \right) = \sin x + c$
B) $x\left( y - \cos x \right) = \sin x + c$
C) $x\left( y\cos x \right) = \sin x + c$
D) $x\left( y - \cos x \right) = \cos x + c$
Explanation
(a)
Given, $\frac{dy}{dx} + \frac{y}{x} = \sin x$
$\therefore$ $IF = e^{\int_{}^{}{\frac{1}{x}\ dx}} = x$
$\therefore$ Solution is $y.x = \int_{}^{}{x\sin x}\ dx + c$
$\Rightarrow$ $xy = - x\cos x + \sin x + c$
$\Rightarrow$ $x\left( y + \cos x \right) = \sin x + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.