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Math Help - differential equations

  1. #1
    Junior Member
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    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 -)?

    thanks
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  2. #2
    Super Member Matt Westwood's Avatar
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    Separate the variables:

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

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