Question

The solution of $2\cos x$ $\frac{dy}{dx}$ $+4y\sin x=\sin 2x$ is:

• A. $2y\cos x=\sec x+c$
• B. $y{\sec }^{2}x=\sec x+c$
• C. $2y\sec x=\sec x+c$
• D. $y\sec x={\sec }^{2}x+c$

Answer 1

Answer: (B)

$y{\sec }^{2}x=\sec x+c$

$2\cos x\frac{dy}{dx}+4y\sin x=2\sin x\cos x$

$\Rightarrow \frac{dy}{dx}+2\tan x.y=\sin x$

$\Rightarrow {\sec }^{2}x\frac{dy}{dx}+\left(2\sec x\right)\left(\sec x\tan x\right)y={\sec }^{2}x\sin x$

$\Rightarrow \frac{d}{dx}\left({\sec }^{2}xy\right)=\sec x\tan x$

$\Rightarrow d\left({\sec }^{2}xy\right)=\sec x\tan xdx$

$\Rightarrow \int ({\sec }^{2}x.y)=\int \sec x\tan xdx+c$

$\Rightarrow y{\sec }^{2}x=\sec x+c$