Question

I.F. of $x\sin x$ $\frac{dy}{dx}$ $+y(x\cos x+\sin x)$ $=\sin$ $x$ is:

• A. $x\cos x$
• B. $x\sec x$
• C. $x\sin x$
• D. $x\csc x$

Answer 1

The correct option is C $x\sin x$

$\frac{dy}{dx}+y\frac{(x\cos x+\sin x)}{x\sin x}=1/x$

$P\left(x\right)=\frac{(x\cos x+\sin x)}{x\sin x}$

$letx\sin x=t\Rightarrow (x\cos x+\sin x)dx=dt$

$\Rightarrow I.F=e^{\int P\left(n\right)dx}=e^{\int \frac{dt}{t}}=e^{logt}=t=x\sin x$