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  • General solution of frac{d y}{d x}+y \tan x=\sec x is (a) y \sec x=\tan x+C

General solution of \frac{d y}{d x}+y \tan x=\sec x is
(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

Answers (1)

Ans: - The answer is the option (a) y sec x = tan x + C

Explanation: -

Here, P=\tan x, Q=\sec x
\therefore \text{I.F.} = e^{\int \tan x \, dx} = e^{\log \sec x} = \sec x \\ \therefore \text{The general solution is } y \sec x = \int \sec x \cdot \sec x \, dx + C \\ \Rightarrow y \sec x = \int \sec^2 x \, dx + C \\ \Rightarrow y \sec x = \tan x + C

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