Question

The integrating factor of the differential equation $\frac{dy}{dx}=\frac{1}{x+y+2}$ is

• A. $e^{x+y+2}$
• B. $e^y$
• C. $e^{-y}$
• D. $\log |x+y+2|$

Answer 1

The correct option is C $e^{-y}$

$\frac{dy}{dx}=\frac{1}{x+y+2}$
$\Rightarrow x+y+2=\frac{dx}{dy}$
$\Rightarrow \frac{dx}{dy}-x=y+2$
Hence, the integrating factor,
I.F. $=e^{\int -dy}=e^{-y}$