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Thread: differential equations

  1. #1
    Junior Member
    Oct 2008

    differential equations

    this seems like it should be simple but again I haven't taken diff. eq. in a while

    how does one solve dP/dt = aP+b (a and b are constants)

    also how would one analyze it as a populations model in the long run in 2 cases (b is - and a is +; b is - and a is -)?

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  2. #2
    MHF Contributor Matt Westwood's Avatar
    Jul 2008
    Reading, UK
    Separate the variables:

    $\displaystyle \int \frac {dP} {aP+b} = \int dt$

    The RHS is simply $\displaystyle t$ (plus a constant) while the LHS you substitute a variable for $\displaystyle aP+b$ and you should get something with a logarithm in in.
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