Question

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

• A. $ y=\cos x+c \sec x$
• B. $y=\cos x+c$
• C. $y=\sin x+c$
• D. $y=\operatorname{cosec} x+c$

Answer 1

Answer: (A)

$\frac{d y}{d x}=y \tan x-2 \sin x$
$\frac{d y}{d x}-y \tan x=-2 \sin x$
I.F. $=e^{-\int \tan x d x}=|\cos x|$
$y \cos x=\frac{\cos 2 x}{2}+k$
$\Rightarrow y=\frac{\cos 2 x}{2 \cos x}+k \sec x \Rightarrow y=\cos x+c \sec x$