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Math Help - Integration using separation of variables.

  1. #1
    Newbie AmberLamps's Avatar
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    Integration using separation of variables.

    Hey guys,

    This is from an econ class so I am really struggling with some of the pure math.

    I need to solve the following differential equation use the separation of variables technique (a,b, and c positive constants):

    dx/dt+ax = b - cx

    What is really confusing to me is what variables I am actually seperating because all I will have on one side is \int dt and it doesn't really seem right to me. But I also can't find any similar examples online.

    thanks for any help.
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  2. #2
    MHF Contributor
    Jester's Avatar
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    Quote Originally Posted by AmberLamps View Post
    Hey guys,

    This is from an econ class so I am really struggling with some of the pure math.

    I need to solve the following differential equation use the separation of variables technique (a,b, and c positive constants):

    dx/dt+ax = b - cx

    What is really confusing to me is what variables I am actually seperating because all I will have on one side is \int dt and it doesn't really seem right to me. But I also can't find any similar examples online.

    thanks for any help.
    Try this

     <br />
\frac{dx}{dt} = b - (a+c)x<br />

    so

     <br />
\frac{dx}{b - (a+c)x} = dt.<br />
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