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: Differential Equations: Second Order Equations

  1. Sep 3, 2011 #1
    1. The problem statement, all variables and given/known data

    Find a second order differential ewuation for which three functions y=2e^-t, y=2te^-t, y=e^(-t+1) are solutions.

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Sep 3, 2011 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Since you didn't show us what you have tried, instead of answering your question directly, I will ask you this:

    Can you solve this de:

    y'' - 4y' + 4y = e2t

    and if so, what method would you use?

    Hint: This isn't an idle question.
  4. Sep 3, 2011 #3


    User Avatar
    Science Advisor

    If those functions were independent, this would be impossible but [itex]e^{-t+ 1}= e^{-t}e^1= e e^{-t}[/itex], a constant times [itex]e^{-t}[/itex] so you really have only two independent solutions.

    Do you know what the "characteristic equation" of a linear differential with constant coefficients is? Such an equation will have [itex]e^{ax}[/itex] and [itex]e^{bx}[/itex] as independent solutions if and only if its characteristic equation is [itex](r- a)(r- b)= 0[/itex].
    Last edited by a moderator: Sep 4, 2011
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook