The general

of $\frac{{dy}}{{dx}} + y\tan x = \sec x$ is

Solution

Given differential equation is

$\frac{{dy}}{{dx}} + y\tan x = \sec x$

which is a linear differential equation Here,

$P = \tan x,Q = \sec x$

$\therefore {\rm{IF}} = {e^{\int {\tan } xdx}} = {e^{\log |\sec x|}} = \sec x$

The general Solution is
$y \cdot \sec x = \int {\sec } x \cdot \sec x + C$

$\Rightarrow$ $y \cdot \sec x = \int {{{\sec }^2}} xdx + C$
$\Rightarrow$ $y \cdot \sec x = \tan x + C$