Question

The solution of the differential equation

$\frac { d y } { d x } = \sec x ( \sec x + \tan x )$is

• A. $y = \sec x + \tan x + c$
• B. $y = \sec x + \cot x + c$
• C. $y = \sec x - \tan x + c$
• D. None of these

Answer 1

Answer: (A)

$y = \sec x + \tan x + c$

Answer 2

$\frac { d y } { d x } = \sec x ( \sec x + \tan x )$ ⇒ $\frac { d y } { d x } = \sec ^ { 2 } x + \sec x \tan x$

Now integrating both sides, we get

$y = \tan x + \sec x + c$.