1. The problem statement, all variables and given/known data https://www.physicsforums.com/attachment.php?attachmentid=65556&stc=1&d=1389570667 For those who can not see the screen shot here is the question... Suppose the population P of rodents satisfies the diff eq dP/dt = kP^2. Initially there are P(0) = 2 rodents, and their number is increasing at the rate of dP/dt = 1 rodent per month when P = 10. How long does it take for the population to reach 105 rodents. 2. Relevant equations 3. The attempt at a solution First I found k by substituting in 10 for p and 1 for dp/dt. 1 = k * 10^2 k = 1/100 Then to solve the differential equation I integrated both sides with respect to t. ∫dp/dt * dt = ∫0.01 * p^2 dt p = 0.01p^2 * t + C I solved for C and found C = 2. Solving for t gives t = 100(p - 2) / p^2 I then plunged in 105 for p and the answer was wrong.