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Homework Help: General solution for DE

  1. May 15, 2010 #1
    1. The problem statement, all variables and given/known data

    y''+4y'+4y= t+exp(-2t)

    find the general solution for the differential equation

    2. Relevant equations



    3. The attempt at a solution

    general solution is sum of complementary function and particular integral

    frist finding complementary function

    y''+4y'+4y=0

    let y=Aexp(mt)

    y'=mA=exp(mt)
    y''=(m^2)A=exp(mt)

    substitute back and get

    ((m^2)+4m+4)Aexp(mt)=0

    m=-2,0

    so complementary function:

    y=Aexp(-2t)+B

    now find particular integral

    y''+4y'+4y=t+exp(-2t)

    try

    y=a+bexp(-2t)
    y'=-2bexp(-2t)
    y''=4bexp(-2t)

    substitute back and get

    4bexp(-2t)-8bexp(-2t)+4(a+bexp(-2t))=t+exp(-2t)
    (4+4-8)bexp(-2t)+4a=t+exp(-2t) !!!!
    so a = t/4 but b will always go to zero i dont know where my mistake is
     
  2. jcsd
  3. May 15, 2010 #2

    LCKurtz

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    Roots are -2, -2.
     
  4. May 15, 2010 #3
    sorry i do not understand you are you proposing (m^2)+4m+4=0 where m= -2,-2?
     
  5. May 16, 2010 #4

    LCKurtz

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    What I am saying is you have the roots wrong, hence the solution wrong.

    m2+4m+4 = (m+2)2

    which has a repeated root of -2. So what is the general solution of the homogeneous equation?
     
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