Suppose dpdt p3 3p2 9p 27 P0 87 What is the limit of Pt

Suppose dp/dt = p3 + 3p2 - 9p - 27, P(0) = -8.7. 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

fixed points are p=-3 and p=3 dp/dt = (p-3)(p+3)^2 for p<3 dp/dt <0 and for p>3 dp/dt > 0 hence as t-> +inf, dp/dt in continuously increasing means p(t)-> +inf also not sure about behaviour as t-> -inf so will not comment.