Question

The solution of the differential equation $\left(1+x^2\right)\frac{dy}{dx}+2xy=\cos x$ 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)

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