The general solution of the differential equation \(\displaystyle\frac{dy}{dx} = (y - 2)\sec^2 x\) is (C is an arbitrary constant)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(y = 2 + Ce^{\tan x}\)
The variables separate:
\( \displaystyle \frac{dy}{y - 2} = \sec^2 x\,dx \)
Integrating both sides, with \(\int \sec^2 x\,dx = \tan x\):
\(\log|y - 2| = \tan x + c\)
\(y - 2 = Ce^{\tan x}\)
\(y = 2 + Ce^{\tan x}\)