Existence, uniqueness of nth-order differential equation

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Homework Statement



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?


Homework Equations



Existence/uniqueness theorem.


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!
 

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