Question:
What is integrating factor of \(\dfrac{dy}{dx} + y\sec x = \tan x\)?
\(\dfrac{dy}{dx} + y\sec x = \tan x\) का समाकलन गुणक (integrating factor) क्या है?
Options:
- \(e^{\sec x}\)
- sec x
- log(sec x + tan x)
- sec x + tan x
- \(e^{\sec x}\)
- sec x
- log(sec x + tan x)
- sec x + tan x
Correct Answer: d)
Explanation:
Linear DE \(\dfrac{dy}{dx} + y\sec x = \tan x\) has \(P = \sec x\).
Integrating factor \(\text{IF} = e^{\int \sec x\,dx} = e^{\ln(\sec x + \tan x)} = \sec x + \tan x\).
समाकलन गुणक \(\text{IF} = e^{\int \sec x\,dx} = e^{\ln(\sec x + \tan x)} = \sec x + \tan x\)।