Let y = y ( x ) be the solution of the differential equation cos x d y d x + 2 y sin x = sin 2 x , x ∈ 0 , π 2 If y ( π / 3 ) = 0 , then y ( π / 4 ) is equal to :

Question

Let y = y ( x ) be the solution of the differential equation cos x d y d x + 2 y sin x = sin 2 x , x ∈ 0 , π 2 If y ( π / 3 ) = 0 , then y ( π / 4 ) is equal to :, 2 - 2, 2 + 2, 2 - 2, 1 2 - 1

MARKS App · Accepted Answer

d y d x + 2 tan x · y = 2 sin x I.F. = e ∫ 2 tan x d x = sec 2 x solution is y · sec 2 x = ∫ 2 sin x · sec 2 x d x + C y sec 2 x = 2 sec x + C ⇒ 0 = 2 . 2 + C ⇒ C = - 4 y sec 2 x = 2 sec x - 4 y π 4 = 2 - 2

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