BITSAT2017MathematicsDifferential EquationsActual
The solution of d y d x = cos x + y + sin x + y , is
Options
- Alog 1 + tan x + y 2 + C = 0
- Blog 1 + tan x + y 2 = x + C
- Clog 1 - tan x + y 2 = x + C
- DNone of the above
Correct answer
B. log 1 + tan x + y 2 = x + C
Step-by-step solution
Put x + y = v and 1 + d y d x = d v d x Therefore, the differential equation reduces to d v d x = 1 + cos v + sin v = 2 cos 2 v 2 + 2 sin v 2 cos v 2 = 2 cos 2 v 2 1 + tan v 2 ⇒   ∫ sec 2 V 2 2 1 + tan v 2 d v = ∫ d x ∴   log 1 + tan x + y 2 = x + C