Question

Integrating factor of $x\frac{dy}{dx}-y=x^4-3x$ is

• A. $x$
• B. $\log x$
• C. $\frac{1}{x}$
• D. $-x$

Answer 1

Answer: (C)

We have,
$x\frac{dy}{dx}-y=x^4-3x$
$\Rightarrow \frac{dy}{dx}-\frac{y}{x}=x^3-3$
$\therefore$ Integrating Factor (IF)$=e^{\int \frac{-1}{x}dx}$
$=e^{-\log x}$
$=e^{\log \frac{1}{x}}=\frac{1}{x}$