If the solution of d y d x - y log e 0 . 5 = 0 , y 0 = 1 , and y x → k , as x → ∞ then k =

Question

If the solution of d y d x - y log e 0 . 5 = 0 , y 0 = 1 , and y x → k , as x → ∞ then k =, ∞, - 1, 1, 0

MARKS App · Accepted Answer

d y d x = y log e 0 . 5 ⇒ d y y = log e 0 . 5 d x Integrating, we get, ln y = ln 0 . 5 x + C Given, y 0 = 1 i.e. C = 0 So, ln y = ln 0 . 5 x ⇒ ln y = - ln 2 x ⇒ y = 2 - x Given, lim x → ∞ 2 - x = k i.e. k = 0

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