Question

Solve $\sin x\frac{dy}{dx}+y\cos x=x\sin x.$

• A. $ysinx=c+x\cos x+\sin x$
• B. $ysinx=c-x\cos x-\sin x$
• C. $ysinx=c-x\cos x+\sin x$
• D. None of these

Answer 1

Answer: (C)

$ysinx=c-x\cos x+\sin x$

$\sin x\frac{dy}{dx}+y\cos x=x\sin x.$
$\frac{dy}{dx}+y\cot x=x,$
$I.F=e^{\int \cot xdx}=e^{\ln \sin x}=\sin x$
Thus required solution is given by,
$y\sin x=\int x\sin xdx+c=c-x\cos x+\sin x$
using by parts.