Question

An integrating factor of the differential equation $xdy - ydx + x^2e^xdx = 0$ 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
$\mid x d y-y d x+x^{2} e^{x} d x=0$
$\Rightarrow x d y+d x\left(x^{2} e^{x}-y\right)=0$
$\Rightarrow \frac{d y}{d x}-\frac{y}{x}=-x e^{x}$
$\therefore IF =e^{\int P d x}=e^{\int-\frac{1}{x} d x}$
$=e^{-\log x} $