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

If the solution of dydx-yloge0.5=0, y0=1, and yx→k, as x→∞ then k=
  1. ∞
  2. -1
  3. 1
  4. 0

Solution

dydx=yloge0.5⇒dyy=loge0.5dx

Integrating, we get,

lny=ln0.5x+C

Given, y0=1

i.e. C=0

So, lny=ln0.5x

⇒lny=-ln2x⇒y=2-x

Given, limx→∞2-x=k

i.e. k=0

Asked in: AP EAMCET 2022 (04 Jul Shift 1)

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