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Math Help - Differential Equation Help!

  1. #1
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    Arrow Differential Equation Help!

    I know this is an simple problem but for the life of me Im lost. I am confused on the second order deriv I dont know how to handle it.

    Verify that y is a solution of the differential equation.

    y = e^-2x;  y'' + y' -2y = 0
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by vodka View Post
    I know this is an simple problem but for the life of me Im lost. I am confused on the second order deriv I dont know how to handle it.

    Verify that y is a solution of the differential equation.

    y = e^-2x;  y'' + y' -2y = 0
    y = e^{-2x}

    y' = -2e^{-2x}

    y'' = 4e^{-2x}

    Now just sub into the differential equation and verify that the left hand side is 0.

    You could even do it like this:
    y' = -2y

    y'' = 4y

    So
    y'' + y' -2y = 0

    4y - 2y - 2y = 0

    -Dan
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  3. #3
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    Quote Originally Posted by topsquark View Post
    y = e^{-2x}

    y' = -2e^{-2x}

    y'' = 4e^{-2x}

    Now just sub into the differential equation and verify that the left hand side is 0.

    You could even do it like this:
    y' = -2y

    y'' = 4y

    So
    y'' + y' -2y = 0

    4y - 2y - 2y = 0

    -Dan
    Duh thanks im an idiot its been awhile since I looked over these.

    Cheers Dan
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