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

Answer: (C)

$\frac{1}{x}$

Answer 2

The given differential equation is:

$x\frac{dy}{dx}-y=2x^{2}$

$⇒\frac{dy}{dx}-\frac{y}{x}=2x$

This is a linear differential equation of the form:

\frac{dy}{dx}+py=Q$$=Q(where p=$$\frac{-1}{x} $and$ $Q=2x$).

The integrating factor(I.F.)is given by the relation,

$e^{∫pdx}$

$∴I.F.=$ $e^{∫\frac{-1}{x}dx}$=$e^{-logx}$=$e^{log(x^{-1})}$=$x^{-1}$=$\frac{1}{x}$

Hence,the correct answer is C.