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Math Help - Differential Equations

  1. #1
    Super Member Aryth's Avatar
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    Differential Equations

    Determine for which values of m the function \phi(x) = e^{mx} is a solution to the given equations:

    (a) \frac{d^2y}{dx^2} + 6\frac{dy}{dx} + 5y = 0

    (b) \frac{d^3y}{dx^3} + 3\frac{d^2y}{dx^2} + 2\frac{dy}{dx} = 0
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  2. #2
    Senior Member vincisonfire's Avatar
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    Just try them.
    m^2 e^{mx}+6m e^{mx} + 5 e^{mx}=0
    Solve for m  m^2 +6m + 5 =0
     m =\frac{-6\pm \sqrt{36-4\cdot 5}}{2} = \frac{-6\pm 4}{2}= -3 \pm 2
    For the next number we have m(m+1)(m+2)=0
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