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: Superposition and variation of parameters

  1. Nov 12, 2008 #1
    1. The problem statement, all variables and given/known data

    y''+2y'+y = 4t^2 - 3 + (e^-t)/t

    of course i evaluated the general soltuion to be c1e^-1t + c2te^-1t

    but now how do you do the right part? i tried y=At^2+Bt+c+1/(Dt+E)*e^-t as a solution but after differentiating it twice and putting it into the eqaution i got...

    (4e^t/Dt+E)-(4De^t/(Dt+E^2))+(2D^2e^t/(Dt+E)^3)+At^2+4At+Bt+2A+2B+C = 4t^2-3+(e^-t)/t

    and i don't know what to do with that. i found a=4 and b=0 and c=-11 but that's about all i did, i'm unsure how to find the rest of the letters to complete the probleme

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 13, 2008 #2

    HallsofIvy

    User Avatar
    Science Advisor

    Since (1/t) e-t is NOT one of the solutions one would expect to get as a solution to a homogeneous d.e. with constant coefficients, "undetermined coefficients" will not work. You titled this "superposition and variation of parameters". Have you tried variation of parameters to get a specific solution for the (1/t)e-t?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...