The general solution of the differential equation $\frac{dy}{dx}+ytanx=sec\, x$ is :
(Where C is constant of integration)
Answer & explanation
Correct answer: option 1
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)
$∫\sec x\frac{dy}{dx}+y\tan x\sec xdx=∫\sec^2 xdx$
$=\sec xy=\tan x+C$