Question

The solution of the differential equation $\frac{dy}{d_X}-y\tan x=e^x\sec x$ is

• A. $y=e^x\cos x+c$
• B. $y\cos x=e^x+c$
• C. $y=e^x\sin x+c$
• D. $y\sin x=e^x+c$

Answer 1

The correct option is B $y\cos x=e^x+c$

$I.F=e^{\int -\tan dx}=e^{-log\sec x}=\cos x$
$\Rightarrow \cos x\frac{dy}{dx}-y\sin x=e^n$
$\Rightarrow \frac{d}{dx}y\cos x=e^x$
$\Rightarrow \int dy\cos x=\int e^{x}dx+c$
$\Rightarrow y\cos x=e^x+c$