Question

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

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

Answer 1

Answer: (A)

$x^2$

Answer 2

We have.
$x \frac{d y}{d x}+2 y=x^{2}$
$\Rightarrow\, \frac{d y}{d x}+\frac{2}{x} y=x$
The above differential equation is a linear differential equation.
$\therefore$ Integrating factor $=e^{\int \frac{2}{x} d x}$
$=e^{2 \log x}$
$=e^{\log\, x^{2}}$
$=x^{2}$