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

The Correct Option is A

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} $