Question

The solution of the differential equation $\left(1+x^2\right) \frac{d y}{d x}+2 x y=\cos x$ is

• A. $y\left(1+x^2\right)=c+\cos x$
• B. $y\left(1+x^2\right)=c+\sin x$
• C. $y=x+c$
• D. $y=\cos x+x^2$

Answer 1

Answer: (B)

$\left(1+x^2\right) \frac{d y}{d x}+2 x y=\cos x$
$\frac{d y}{d x}+\frac{2 x}{1+x^2} y=\frac{\cos x}{1+x^2}$
$I . F .=1+x^2$
$\frac{d}{d x}\left(y\left(1+x^2\right)=\cos x\right.$
$\left(1+x^2\right) y=\sin x+c$