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1)

Let  the population of rabbits surviving at a time t be governed by the differential equation  dp(t)dt=12p(t)200.If  p(0)=100, then  p(t) is equal to 


A) 400300et2

B) 300200et2

C) 600500et2

D) 400300et2

Answer:

Option A

Explanation:

Given, differential  equation dpdt12p(t)=200 is linear ndifferential equation 

 Here,   p(t)=12,Q(t)=200

IF=e(12)dt=et/2

 Hence, solution is

          p(t).IF=Q(t)IFdt

   p(t).et/2=200.et2dt

                p(t).et/2=400.et2+K

              p(t).=400+ke12

if p(0)=100, then k=-300

   400300et2