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: 2rd order ODE

  1. Oct 15, 2006 #1
    Solve the given initial value problem.
    9y"-12y'+4y=0 y(0)=2 y'(0)=-1

    9r^2-12r +4=0
    so r=2/3
    so my general solution would be y(t)=c_1e^2/3t +c_2e^2/3t
    Whenever I try to use the initial conditions I can't get them to work. One disappears.
    Is my general solution even right?
  2. jcsd
  3. Oct 15, 2006 #2


    User Avatar
    Homework Helper

    You only have one linearly independent solution there. When you get a double root like that, the other solution is given by, in this case, [itex]t e^{2/3 t} [/tex]. You can verify this by plugging it into the DE.
  4. Oct 15, 2006 #3
    I get it.. thanks a lot!!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook