Question

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

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

Answer 1

The correct option is D $y\sec x=c+\sin x$

I.F$e^{\int \tan xdx}=e^{log\sec x}=\sec x$
$\Rightarrow \sec x\frac{dy}{dx}+y\sec x\tan x=\cos x$
$\Rightarrow \frac{d}{dx}\left(y\sec x\right)=\int \cos xdx+c$
$\Rightarrow y\sec x=\sin x+c$