Question

The solution of differential equation $\frac{dy}{dx}=\cos x(2-y\mathrm{cosec}x)$ is

• A. $y=\tan \frac{x}{2}+\cot \frac{x}{2}+C$
• B. $y=\frac{1}{\sqrt{2}}\sec \frac{x}{2}+\sqrt{2}\cos \frac{x}{2}+C$
• C. $y=\sin x+C\mathrm{cosec}x$
• D. $y=\sin x-\cos x+C$

Answer 1

Answer: (C)

$\frac{dy}{dx}=2\cos x-y\cot x$
$\frac{dy}{dx}+y\cot x=2\cos x$
IF $=e^{\int \cot xdx}=e^{\ell n\sin x}=\sin x$
complete solution
$y\cdot \sin x=\int \sin x\cdot 2\cos xdx$
$y\sin x={\sin }^{2}x+C$
$y=\sin x+C\mathrm{cosec}x$