Let the solution y = y ( x ) of the differential equation d x d y − y = 1 + 4 sin x satisfy y ( π ) = 1 . Then y ( 2 π ) + 10 is equal to ______

Question

Let the solution y = y ( x ) of the differential equation d x d y ​ − y = 1 + 4 sin x satisfy y ( π ) = 1 . Then y ( 2 π ​ ) + 10 is equal to ______

TestHub · Accepted Answer

​ y e − x = ∫ ( e − x + 4 e − x sin x ) d x y e − x = − e − x − 2 ( e − x sin x e − x cos x ) + C y = − 1 − 2 ( sin x + cos x ) + c e x ∵ y ( π ) = 1 ⇒ c = 0 y ( π /2 ) = − 1 − 2 = − 3 Ans = 10 − 3 = 7 ​

Mathematics - Differential Equation Question with Solution | TestHub

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