Let y = y ( x ) be the solution of the differential equation d y d x = 2 y + 2 sin x - 5 x - 2 cos x such that y ( 0 ) = 7 . Then y ( π ) is equal to

Step-by-step solution

d y d x - 2 x y = 2 2 sin   x - 5 x - 2 cos   x I F = e - x 2 So, y   e - x 2 = ∫ e - x 2 2 x 2 sin   x - 5 - 2 cos   x   d x ⇒ y · e - x 2 = e - x 2 5 - 2 sin x + C y = 5 - 2   sin x + C · e x 2 Given at x = 0 ,   y = 7 ⇒ 7 = 5 + C ⇒ C = 2 So, y = 5 - 2   sin   x + 2 e x 2 Now at x = π y = 5 + 2 e π 2