The solution of the differential equation dy dx = x( x + x)is - Vidyadip

MCQ

The solution of the differential equation $\frac{{dy}}{{dx}} = \sec x(\sec x + \tan x)$is

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

✓

Answer

Correct option: A.

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

a
(a) $\frac{{dy}}{{dx}} = \sec x(\sec x + \tan x)$ ==> $\frac{{dy}}{{dx}} = {\sec ^2}x + \sec x\tan x$

Now integrating both sides, we get $y = \tan x + \sec x + c$.

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