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Homework Help: Existence, uniqueness of nth-order differential equation

  1. Sep 9, 2010 #1
    1. The problem statement, all variables and given/known data

    Let [tex]p(t)[/tex] and [tex]q(t)[/tex] be continuous on [tex]\mathbb{R}[/tex]. Is it possible for the function [tex]y=e^t-(t^2/2)-t-1[/tex] to be a solution of the equation [tex]y''+p(t)y'+q(t)y=0[/tex] ? Why or why not?


    2. Relevant equations

    Existence/uniqueness theorem.


    3. The attempt at a solution

    Supposedly I should let [tex]x=(x_0,x_1)^T[/tex], where [tex]x_0=y[/tex] and [tex]x_1=y'[/tex]. This gives us [tex]x'=(x_1,-p(t)x_1-q(t)x_0)^T[/tex].

    Unfortunately, I don't know how to check for Lipschitz continuity of a vector-valued function. Even if I could do that, I still wouldn't know what to do next!

    Needless to say, I'm pretty lost on this one. Any help would be much appreciated!
     
  2. jcsd
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