Solve the following differential equation:

Given:

Dividing both sides by cos² x, we get

… (1)

Which is a linear differential equation of the form

Here P=sec² x, Q = tan x. sec² x

∴ Solution is

Putting tan x = t ⇒ sec² x dx = dt

⇒ ye^t = te^t – e^t + c = e^t (t – 1) + c

Since tan x = t,

∴ y = tan x – 1 + ce^{-tan x}