The general solution of the differential equation \(\displaystyle\frac{dy}{dx}+y\tan x=\sec x\)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(y\sec x- \tan x = c\), where c is an arbitrary constant
This is a linear differential equation \(\frac{dy}{dx} + Py = Q\) with \(P = \tan x\) and \(Q = \sec x\). The integrating factor is
\( \displaystyle \text{I.F.} = e^{\int \tan x\,dx} = e^{\log|\sec x|} = \sec x \)
The solution is \(y \cdot \text{I.F.} = \int Q \cdot \text{I.F.}\,dx + c\):
\( \displaystyle y\sec x = \int \sec^2 x\,dx + c \)
\(y\sec x = \tan x + c\)
\(y\sec x - \tan x = c\)
NCERT Exemplar:
Differential Equations
