The general solution of the differential equation $\frac{dy}{dx}+ytanx=sec\, x$ is :

(Where C is constant of integration)

$ysecx = tanx +C$

The correct answer is Option (1) → $y\sec x = \tan x +C$

$\frac{dy}{dx}+y\tan x=\sec x$  ...(1)

so $I.F.=e^{∫\tan xdx}=e^{\log\sec x}=\sec x$

Multiplying (1) by I.F. and integrating wrt (x)

$∫\sec x\frac{dy}{dx}+y\tan x\sec xdx=∫\sec^2 xdx$

$=\sec xy=\tan x+C$