Question

The solution of differential equation $\frac{d^{2}y}{d{x}^2}=x\sin x$ is

• A. $y=-x\sin x-2\cos x+cx+d$
• B. $y=x\sin x+2\cos x+cx+d$
• C. $y=2\cos x+cx+d$
• D. None of the above

Answer 1

Answer: (A)

$y=-x\sin x-2\cos x+cx+d$

Given that $\frac{d^{2}y}{d{x}^2}=x\sin x$
On integrating w.r.t $x$, we get
$\frac{dy}{dx}=-x\cos x+\int xdx+C=-x\cos x+\sin x+C$
Again integrating, we get
$y=-x\sin x-2\cos x+cx+d$