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Math Help - How to solve this differential equation?

  1. #1
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    How to solve this differential equation?

    Hi all,

    I'm trying to (re-)teach myself differential equations, and I've run into a snag. Say I have a differential equation which includes the solution on the RHS. How can I solve this, I think I can put it into standard form, but then I get stuck. Say I have

    $$\frac{dP}{dt}=.3P-20$$

    and where

    $$P(0)=35$$

    where P is the function I'm trying to obtain. I would think I could put this in standard form like so

    $$\frac{dP}{dt}-.3P=-20$$

    with an integrating factor of

    $$v(t)=\exp{(-\int.3dt)}=\exp(-.3t)$$

    So I'd get

    $$\exp{(-.3t)}(\frac{dP}{dt}-.3P)=-20\exp{(-.3t)}$$

    I know that the solution is the following, but I'm not sure of how to get there.

    $$P(t)=(20-20\exp{(.3t)}+.3(35)\exp{(.3t)}/.3)$$

    Any help would be appreciated.
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  2. #2
    MHF Contributor
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    Re: How to solve this differential equation?

    Hey joeschmo.

    You should probably look at this:

    Integrating factor - Wikipedia, the free encyclopedia

    Note that you can also use the fact that dP/(0.3P - 20) = dt and integrate both sides to get the same answer as you would obtain from using
    integrating factors.
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  3. #3
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    Re: How to solve this differential equation?

    Ah, that does it. I guess I can solve this by separation of variables. Thanks for the hint. Still didn't get there with the integrating factor yet but I'll give it another crack later.
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