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 Equations Question

  1. Jun 19, 2013 #1
    Can anyone tell me how the book arrived at the portion that I underlined in the paint document?
     

    Attached Files:

  2. jcsd
  3. Jun 20, 2013 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    It's using the fact that
    [tex] \mathfrak{L}\left( \sum a_i \frac{d^k}{dx^k} y \right) = \sum a_i \mathfrak{L} \left( \frac{d^k}{dx^k} y \right) [/tex]
    And that if you take the Laplace operator of the kth derivative of y you get sk L(y) plus some values of y and its derivatives at 0 (more specifically the general differentiation property at http://en.wikipedia.org/wiki/Laplace_transform#Properties_and_theorems)

    The ak coefficients that were next to the differential operators stick around and multiply the sk L(y) guys, meaning you get exactly q(s) out if you started with q(D), but the polynomial terms depend on the derivatives at zero so is hard to calculate what its relationship with q(s) is
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Differential Equations Question
Loading...