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) 400−300et2 B) 300−200et2 C) 600−500et2 D) 400−300et2 Answer: Option AExplanation:Given, differential equation dpdt−12p(t)=−200 is linear ndifferential equation Here, p(t)=−12,Q(t)=−200 IF=e∫−(12)dt=e−t/2 Hence, solution is p(t).IF=∫Q(t)IFdt p(t).e−t/2=∫−200.e−t2dt p(t).e−t/2=400.e−t2+K ⇒ p(t).=400+ke−12 if p(0)=100, then k=-300 ⇒ 400−300et2