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Math Help - Homogeneous Equations with Constant Coefficients

  1. #1
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    Homogeneous Equations with Constant Coefficients

    Find the general solution of the given differential equation.

    y'' + 5y' = 0

    The answer is y = C1 + C2*e^(-5t)

    I don't know where to begin with this, unfortunately I missed this lecture. Thanks.
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  2. #2
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    Quote Originally Posted by pakman View Post
    Find the general solution of the given differential equation.

    y'' + 5y' = 0

    The answer is y = C1 + C2*e^(-5t)

    I don't know where to begin with this, unfortunately I missed this lecture. Thanks.
    The characheeristic equation:

    k^2+5k=0

    k(k+5)=0

    k=0 or k=-5

    Thus,

    e^0 = 1 and e^{-5t} are solutions.

    All linear combinators are,

    C_1(1)+C_2*e^{-5t}
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