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

• ${e^{ - x}}$

• ${e^{ - y}}$

• $\cfrac{1}{x}$

• $x$

option c is correct

The given equation can be written as $\cfrac{{dy}}{{dx}} - \cfrac{y}{x} = 2x$

which is a linear equation of type $\cfrac{{dy}}{{dx}} + Py = Q$

Where, $P = - \cfrac{1}{x},Q = 2x$

$\therefore$ ${\rm{I}}{\rm{.F}}{\rm{.}} = {e^{\int P dx}} = {e^{\int { - \cfrac{1}{x}dx} }} = {e^{ - \log x}} = {e^{\log {x^{ - 1}}}} = {x^{ - 1}} = \cfrac{1}{x}$