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: Getting the particular solution of this differential equation.

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


    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


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