# Existence, uniqueness of nth-order differential equation

## Homework Statement

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

## Homework Equations

Existence/uniqueness theorem.

## The Attempt at a Solution

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

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!