Question

The integrating factor of the differential equation $x\frac{dy}{dx}+2y=x^2$ is $(x\ne 0)$

• A. $x^2$
• B. $\log |x|$
• C. $e^{\log x}$
• D. $x$

Answer 1

The correct option is A $x^2$

the equation $x\frac{dy}{dx}+2y=x^2$ is $(x\ne 0)$ can be re-written as $\frac{dy}{dx}+\left(\frac{2}{x}\right)y=x$

$\text{I.F.}=e^{\int \frac{2}{x}dx}$

$\Rightarrow \text{I.F.}=e^{\log x^2}$

$\Rightarrow \text{I.F.}=x^2$