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Math Help - Integration of differential equations

  1. #1
    Junior Member
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    Integration of differential equations

    I am trying to integrate a differential equation

     \frac{-0.1}{-0.3-0.1u}du = -0.1dx

    I would like to show the integral in the form of u(x) = ........

    Any ideas of where i can start and what methods i can use to solve this differential equation?
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  2. #2
    MHF Contributor Calculus26's Avatar
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    On the left let z = -.3 -.1 u

    Then dz = -.1 du

    you have int (dz/z) = ln(z) = ln ( -.3 -.1u) = -.1 x + c

    exponentiate -.3 -.1u = e^(-.1x+c) = e^(-.1x)e^(c) =C e^(-.1x)

    since e^c is just a constant

    -.3 - C e^(-.1x) = .1u

    -3 - C e^(-.1x) = u(x)

    you may have wondered why I dropped the abs value from the ln integral.

    based on the initial condition C will take care of any sign.
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