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Math Help - Verify Solution

  1. #1
    Member moonnightingale's Avatar
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    Verify Solution

    the book says

    Determine for which values of m the function
    y=exp(mx) is solution of differential equation

    y'' + 6y' + 5y=0

    Plz help me
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  2. #2
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    Re: Can u helpmefor this question of differential equations

    Hello, moonnightingale!

    \text{Determine for which values of }m\text{ the function }y\,=\,e^{mx}
    . . \text{is solution of differential equation: }\;y'' + 6y' + 5y\:=\:0

    In effect, you are given a differential equation and an answer.
    . . You are asked to check the answer.
    You don't know how to do that?


    Differentiate: . \begin{Bmatrix} y &=& e^{mx} \\ y' &=& me^{mx} \\ y'' &=& m^2e^{mx} \end{Bmatrix}


    Substitute into the differential equation:
    . . m^2e^{mx} + 6me^{mx} + 5e^{mx} \:=\:0


    Divide by e^{mx}\!:
    . . m^2 + 6m + 5 \:=\:0


    Can you finish it now?

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  3. #3
    MHF Contributor

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    Re: Can u helpmefor this question of differential equations

    It is important to note that e^{mx} is never 0 so you can divide by it.
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