Thread: Solving IVP

The birth rate of B(t) of a population P(t) decreases exponentially with time, so that B(t)=B0e^at where a,B>0. Therefore the population dynamics are governed by the differential equation:

dP/dt=B(t)P where P(0)=P0

Solve the above initial value problem to find an expression for P(t) in terms of P0,a,B. Use this expression to deduce the behavior of P(t) as t->infinity.

**I know people would like to advice me on the steps to take, but I would understand alot better if I was shown what the steps were, so I can understand the steps on my own**

Originally Posted by NFS1

The birth rate of B(t) of a population P(t) decreases exponentially with time, so that B(t)=B0e^at where a,B>0. Therefore the population dynamics are governed by the differential equation:

dP/dt=B(t)P where P(0)=P0

Solve the above initial value problem to find an expression for P(t) in terms of P0,a,B. Use this expression to deduce the behavior of P(t) as t->infinity.

**I know people would like to advice me on the steps to take, but I would understand alot better if I was shown what the steps were, so I can understand the steps on my own**

The equation is separable, so divide both sides by P, then integrate.

what is the resulting expression after integration??

Why don't you tell me?