Question

An integrating factor of the differential equation $xdy-ydx+x^2{e}^{x}dx=0$ is

• A. $\frac{1}{x}$
• B. $log\sqrt{1+x^2}$
• C. $\sqrt{1+x^2}$
• D. $x$
• E. $\frac{1}{1+x^2}$

Answer 1

Answer: (A)

Given differential equation i
$\mid xdy-ydx+x^2{e}^{x}dx=0$
$\Rightarrow xdy+dx\left(x^2{e}^x-y\right)=0$
$\Rightarrow \frac{dy}{dx}-\frac{y}{x}=-x{e}^x$
$\therefore IF=e^{\int Pdx}=e^{\int -\frac{1}{x}dx}$
$=e^{-\log x}$