Question

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

• A. $e^{{\tan }^{-1}x}$
• B. $e^{{\sin }^{-1}x}$
• C. $e^{{\cos }^{-1}x}$
• D. $e^{{\cot }^{-1}x}$

Answer 1

The correct option is A $e^{{\tan }^{-1}x}$

$(1+x^2)\frac{dy}{dx}+y=x\Rightarrow \frac{dy}{dx}+\frac{y}{1+x^2}=\frac{x}{1+x^2}$
Integrating factor
$=e^{\int \frac{1}{1+x^2}dx}=e^{{\tan }^{-1}x}$