Question

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

Answer: (B)

$y\cos x=e^x+c$

Given linear differential equation is
$\frac{dy}{dx}-y\tan x=e^x\sec x$
$\therefore IF=e^{-\tan xdx}=e^{-\log \sec x}=\frac{1}{\sec x}$
$\therefore$ Complete solution is
$y\cdot \frac{1}{\sec x}=e^x\sec x\cdot \frac{1}{\sec x}dx$
$\Rightarrow \frac{y}{\sec x}=e^x+c$
$\Rightarrow y\cos x=e^x+c$