Q. 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\$
Explanation
(b)
Given, $\frac{dy}{dx} - y\tan x = e^{x}\sec x$
$\therefore$ $IF = e^{- \int_{}^{}{\tan x\ dx}} = e^{- \log{\sec x}} = \frac{1}{\sec x}$
$\therefore$ Complete solution is
$\Rightarrow$ $y.\frac{1}{\sec x} = \int_{}^{}e^{x}\sec x.\frac{1}{\sec x}\ dx$
$\Rightarrow \$ $\frac{y}{\sec x} = e^{x} + c$
$\Rightarrow$ $y\cos x = e^{x} + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.