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Math Help - Solving IVP

  1. #1
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    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**
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  2. #2
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    Re: Solving IVP

    Quote Originally Posted by NFS1 View Post
    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.
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  3. #3
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    Re: Solving IVP

    what is the resulting expression after integration??
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  4. #4
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    Re: Solving IVP

    Why don't you tell me?
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