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Getting the particular solution of this differential equation.

  1. Oct 11, 2007 #1
    1. The problem statement, all variables and given/known data

    y''-2y'-3y=-3t*e^(-t)

    2. Relevant equations

    Has to be done with method of undetermined coefficients

    3. The attempt at a solution

    the chacteristic equation is: c1*e^(3t) + c2*e^(-t)

    my attempt at Yp is (a*t+b)*e^(-t)... so ya thats not it. i tried many versions and i keep on getting a = 3t/4.

    the book has the answer as y=c1*e^(3t) + c2*e^(-t)+(3/16)*t*e^(-t)+(3/8)*t^2*e^(-t)
     
  2. jcsd
  3. Oct 11, 2007 #2
    Your homogeneous equation has a solution that is of the form of one of your terms in the particular solution. I suggest a similar guess, with a tweak.
     
  4. Oct 12, 2007 #3

    HallsofIvy

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    Science Advisor

    Since e3t is already a solution to the homogeneous equation, you need to multiply your first "guess" by t.
     
  5. Oct 12, 2007 #4
    thx i successfully got the answer. At first i tried to get that to work, but then it came to the part where you gotta solve for like 3 variables, like a, b, and t... and while glancing over to my calculus book, which has a better writup on diffeq then my diffeq book lol, i saw how you had to deal with this by equating the coeffecients. i dont remember this problem i posted about but it was like you had to seperate it where t(a + b) + (a - b) = 3t. and did a + b = 3, and a - b = 0, and solve for a and b that way. it's interesting that that even works cause my ti89 can't do it, which is shocking lol
     
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