Pretty straight forward separable equations.
With b> 0 you have and with b= 0, .
Those are easy to integrate.
Birth rates of animal populations are typically not constant but vary periodically with the passing seasons. Find an expression for P(t) if the population dynamics are governed by the differential equation:
dP/dt=(k+bcos2(pi)t)P
Where 't' is in years and k>0. Compare the growths of a population where b>0 with one where b=0 at the end of a full year. Both populations have the same initial value Po