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High order differential equations: undetermined coefficients

  1. Dec 6, 2014 #1
    1. The problem statement, all variables and given/known data

    If the method of undetermined coefficients is used to find a particular solution
    yp (t) to the differential equation y'''-y'=te^(-t)+2cos(t) should
    have the form: ?


    2. Relevant equations


    3. The attempt at a solution
    LHS

    r^3-r=0

    roots= 0, 1

    y_c(t)=c_1e^t


    RHS

    te^(-t)+2cos(t)

    (At+B)e^(-t)+Ccos(t)+Dsin(t)

    correct answer given however is

    t(At + B)e^(-t) + C cos(t) + D sin(t)

    I don't know how that t in front got there.. It would make sense if my LHS gave e^-t. but i dont think it does.


    Thanks
     
  2. jcsd
  3. Dec 6, 2014 #2

    dwn

    User Avatar

    Hello dmoney,

    Your LHS should be yc(t) = c1et + c2e(0*t) = c1et + c2

    missed that .... c3e-t
     
  4. Dec 6, 2014 #3

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Your characteristic equation is third order in r. How many roots are there?
     
  5. Dec 6, 2014 #4
    right... 3 roots...

    so r^3-r=0

    r=0, r=1, and.... r=-1

    -1-(-1)=0

    I always get stuck on the stupidest mistakes.

    I really appreciate it! thanks
     
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