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Math Help - Differential equation y + 6y + 12y+ 8y = 12e^(-2x)

  1. #1
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    Differential equation y + 6y + 12y+ 8y = 12e^(-2x)

    y’’’ + 6y’’ + 12y’+ 8y = 12e^{-2x}

    EDIT: Hey, why don't the primes show up? Here's it without using the code
    y’’’ + 6y’’ + 12y’+ 8y = 12e^(-2x)

    trying using both method of undetermined coefficient & variation of parameters.

    Y’’’ + 6y’’ + 12y’+ 8y = 12e^(-2x)? - Yahoo! Answers
    Last edited by mathwizard; June 16th 2008 at 07:10 PM.
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  2. #2
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    Quote Originally Posted by mathwizard View Post
    y’’’ + 6y’’ + 12y’+ 8y = 12e^(-2x)
    The first step is to solve y'''+6y''+12y'+8y = 0 the charachteristic equation is k^3 + 6k^2 + 12k+8 = 0. This factors as (k+2)^{2} = 0. Thus, the general solution is c_1e^{-2x}+c_2xe^{-2x}+c_3x^2e^{-2x}. To find the particular solution we would look for a solution of the form Ae^{-2x} but since this is included amongst the general we need to look for a solution of the form Ax^3e^{-2x}.
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