Question

The integrating factor of the differential equation $x\frac{dy}{dx}-y=2x^2$

• A. $e^{-x}$
• B. $e^{-y}$
• C. $\frac{1}{x}$
• D. x

Answer 1

Answer: (C)

$x\frac{dy}{dx}-y=2x^{2}or\frac{dy}{dx}-\frac{y}{x}=2x$
$I.F.=e^{\int \frac{-1}{x}dx}=e^{-\log x}=e^{-\log x}=e^{\log \frac{1}{x}}=\frac{1}{x}$