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Math Help - Reduction of Order

  1. #1
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    Reduction of Order

    y''-2y'+y=0 ; With Solution y = e^x
    So far I got:

    let y=f(x)*v = e^xv

    y'=e^xv+e^xv'

    y''=e^xv+e^xv'+e^xv'+e^xv''

    substituting that into y''-2y'+y=0 gets=

    e^xv'' and then v''=w' we get

    e^xw' not sure where to go from here though : (
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  2. #2
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    Quote Originally Posted by Link88 View Post
    y''-2y'+y=0 ; With Solution y = e^x
    So far I got:

    let y=f(x)*v = e^xv

    y'=e^xv+e^xv'

    y''=e^xv+e^xv'+e^xv'+e^xv''

    substituting that into y''-2y'+y=0 gets=

    e^xv'' and then v''=w' we get

    e^xw' not sure where to go from here though : (

    Since this is a second order linear constant coefficient ODE, find the characteristic equation

    m^2 - 2m + 1 = 0

    (m - 1)^2 = 0

    m = 1, a repeated root.


    So your solution to the DE will have the form

    y = C_1e^{x} + C_2xe^{x}.


    You will need to use some intial conditions to find the constants.
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