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Math Help - Separable ODE

  1. #1
    Ant
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    Separable ODE

    Hi,

    I'm sure this is straight forward I'm just having a mental block:

    I'm trying to solve:

    \frac{dv}{dt}=1+(K+1)v

    should only need the first step or a hint!
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  2. #2
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    Re: Separable ODE

    There might be a simpler method but you can solve it like in the example here Examples of differential equations - Wikipedia, the free encyclopedia
    Where p(x)= -(k+1) and q(x)= 1
    Thanks from Ant
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  3. #3
    Ant
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    Re: Separable ODE

    Thanks, my lecture notes said it was separable, but I'm pretty sure it's actually not!
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  4. #4
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    Re: Separable ODE

    The equation can be solved by the variables separable method,

    write it as \int \frac{dv}{1+(K+1)v}=\int dt.

    It integrates directly to

    \frac{1}{K+1}\ln (1+(K+1)v)=t+C.
    Thanks from Shakarri
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  5. #5
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    Re: Separable ODE

    Lol can't believe I missed that. I've recently been doing a lot of problems with the more complicated method.
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