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)

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