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Math Help - Simple ODE need to double check if correct

  1. #1
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    Simple ODE need to double check if correct

    Can some one tell me if i am correct or completely off

    \frac{dP}{dA} = h(1-P)-rP with initial condition P(0)=1

    here r and h are constants.

    \frac{dP}{dA} = h(1-P)-rP

    by substitution

    \frac{log(h-ph-pr)}{h+r}=-A+C

    therefore



    h-ph-pr=Ce^{-A(h+r)}

    p=\frac{h}{h+r}-Ce^{-A(h+r)}

    using condition p(0)=1

    C=\frac{h}{h+r}-1}

    the solution is

    p=\frac{h}{h+r} - \frac{h}{h+r}e^{-A(h+r)} + e^{-A(h+r)}

    which can be factored as


    p=\frac{h+re^{-A(h+r)}}{h+r}


    is this correct?

    this is in reference to the paper in Malaria Journal Smith et al 2007 'Standardising estimates of the Plasmodium Falciparum parasire rate' this equation is listed on page 3 and i cant recapture their solution

    their solution is


    p=\frac{h}{h+r} (1-e^{-A(h+r)})

    I must be doing something stupid
    Last edited by chogo; September 18th 2011 at 01:55 PM.
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  2. #2
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    Re: Simple ODE need to double check if correct

    In the referenced paper, the solution corresponds to the condition p(0)=0
    while your solution corresponds to p(0)=1.
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  3. #3
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    Re: Simple ODE need to double check if correct

    Thank you JJacquelin. They have miss specified the initial condition in the paper then.

    Thanks for your time and input
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