Question

The Integrating Factor of the differential equation $x\frac{dy}{dx}-y=2x^2$ is:

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

Answer 1

The correct option is C $\frac{1}{x}$

For Liner equation $\frac{dy}{dx}+Py=Q$

Integrating factor is given by $I=e^{\int Pdx}$

So here, $P=\frac{-1}{x}$

$I=e^{\int \frac{-1}{x}dx}$
$I=e^{-\ln \left(x\right)}$
$I=e^{\ln \left(\frac{1}{x}\right)}$

$\Rightarrow I=\frac{1}{x}$