1. Not finding help here? Sign up for a free 30min 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!

Differential equation root

  1. Mar 28, 2012 #1
    1. The problem statement, all variables and given/known data
    y''-4y'+4y=x*e2x

    I'm trying to find the homogenous solutions of this equation. I know there are two, but I can only find one.

    YH=> y''-4y'+4y=0

    2. Relevant equations



    3. The attempt at a solution

    y''-4y'+4y=0
    Using the characteristic function:
    a2-4a+4=a <=> (a-2)2=0
    Therefore
    C1*e2x
    is a solution. However, since this is a 2nd order differential equation, I should have two. I can solve the rest of the equation if I can find the 2nd solution. I've tought about it a lot but can't manage to find the answer... All help will be appreciated.
    Thanks!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 28, 2012 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    If you have a double root 2, then C2*x*e^(2x) is also a homogeneous solution.
     
    Last edited: Mar 28, 2012
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook