Suppose dpdt p2 4p 4 P0 71 What is the limit of Pt as t in

Suppose dp/dt = -p2 +4p -4, P(0) = 7.1. What is the limit of P(t) as t increases to + infinity (if P(t)explodes in finite time, enter + Inf or - Inf)? What is the limit of P(t) as t decreases to - infinity (if P(t)explodes in finite time, enter + Inf or - Inf)?

Solution

dp/dt=-(P-2)^2 dP/(P-2)^2=-dt -1/(P-2)=-t-c (c is a constant) hence 1/(p-2) = t+c meaning p=2+1/(t+c) p(0) = 2+1/c = -7.1 -1/c=9.1 c=-1/9.1=-0.10989011 = -k (say) p(t) = 2+1/(t-k) as t-> +inf or -inf, 1/(t-k) tends to 0 hence p(t) tends to 2 in both the cases