The integrating factor of the differential equation $x \frac{d y}{d x}-y=\sin x$ is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\frac{1}{x}$
$x \frac{d y}{d x}-y=\sin x$
$⇒\frac{d y}{d x}-\frac{1}{x}=\frac{\sin x}{x}$
I.F. = $e^{\int P(x)dx}e^{-\int\frac{1}{x}dx}=e^{\log_e(\frac{1}{x})}=\frac{1}{x}$