Question

Let y = y(x) be the solution of the differential equation dy/dx = 2 (y + 2 sin x – 5) x – 2 cosx such that y(0) = 7. Then y(π) is equal to :

(1) \(2e^{\pi^2}\) + 5

(2) \(e^{\pi^2}\)+ 5

(3) \(3e^{\pi^2}\)+ 5

(4) \(7e^{\pi^2}\)+ 5

Answer 1

Option : (1). \(2e^{\pi^2}\) + 5

dy/dx - 2xy = 2(2sin x - 5) x - 2cosx