1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member


    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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook