Question

Solve the differential equation: $\frac{dy}{dx}-y\tan x=e^x\sec x$

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

Answer 1

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

$\frac{dy}{dx}-y\tan x=e^x\sec x$ ...(1)
Here $P=-\tan x\Rightarrow \int Pdx=-\int \tan xdx=-\log \sec x=\log \cos x$
$\therefore I.F.=e^{\log \cos x}=\cos x$
Multiplying (1) by $I.F.$, we get
$\cos x\frac{dy}{dx}-y\sin x=e^x$
Integrating both sides, we get
$y\cos x=\int e^{x}dx+c=e^x+c$