CUET · MATHS · PYQ PAPER 2023
The general solution of the differential equation \(\frac{d y}{d x}+y \tan x=\sec x\) is :
(Where \(C\) is constant of integration)
- A y sec x = tan x + C
- B y tan x = sec x + C
- C tan x = y tan x + C
- D x sec x = tan y + C
Answer & Solution
Correct Answer
(A) y sec x = tan x + C
Step-by-step Solution
Detailed explanation
IF \( = e^{\int \tan x dx} = e^{\ln|\sec x|} = \sec x \) \(y \cdot \text{IF} = \int Q(x) \cdot \text{IF} dx + C \) \(y \sec x = \int \sec x \cdot \sec x dx + C \) \(y \sec x = \int \sec^2 x dx + C \) \(y \sec x = \tan x + C \)
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