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: Second order linear differential operator

  1. Aug 5, 2009 #1
    1. The problem statement, all variables and given/known data
    Suppose that L is a second order linear differential operator over the interval J, that f is a function defined on J, and that the function v has the property that

    Lv = f on J

    (a) Show that if y = u + v and that Lu = 0 on J, then Ly = f on J
    (b) Show that if Ly = f on J, then y = u + v for some u such that Lu = 0 on J
    2. Relevant equations
    None that apply
    3. The attempt at a solution
    Well unfortunately this one I was unable to attempt because i am not even sure what it is asking, this professor I have tends to deviate from the book.
  2. jcsd
  3. Aug 5, 2009 #2
    (a) If L is linear, then L(u+v)=Lu+Lv. So if we have Lu=0, then


    (b) Since L is linear, then there is a zero vector u with Lu=0 and 0+y=y. Choose u=0 and v=y. Then u+v=0+y=y.
  4. Aug 5, 2009 #3
    Thanks man I would never figure that out!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook