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: Help solving the Initial Value Problem

  1. Apr 1, 2012 #1
    1. The problem statement, all variables and given/known data
    y''-4y'+4y=0 , y(1)=1 and y'(1)=1

    3. The attempt at a solution

    Auxiliary equation: r2-4r+4=0

    I tried factoring 2 different ways:




    y(1)=c1e2+c2e2=1 ---eq(1)


    ...c2=1/(2e2)-c1 ---eq(2)

    sub eq(2) into eq(1) --> 1/2=1

    method 2:


    r=-4, r=0

    y(1)=c1e-4+c2=1 ---eq(1)


    sub eq(2) into eq(1) --> c2=5/4

    solution equation:

    =1..... which doesnt seem correct

    i checked the solutions on wolframalpha and it solves it using the first method, but ends up with:

    y2=c2e2t *t

    can someone explain to me why the extra t shows up in y2? Thanks.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
    Last edited: Apr 1, 2012
  2. jcsd
  3. Apr 1, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

    hi middieman147 :smile:

    (i don't understand your second method at all :confused:)
    it isn't an x, it's a t

    when a root b is repeated (in the auxiliary equation), the two independent solutions are ebt and tebt

    if it's repeated n times, the n independent solutions are ebt tebt … tn-1ebt
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook