Can somebody help me to solve this problem:
Given an ODE $\displaystyle x'=f(t,x)$ continous and lokally lipschitz for x. $\displaystyle x(t), t \geq t_0$ is a solution to the initial value problem $\displaystyle x(t_0)=x_0$. $\displaystyle x_1(t) $ and $\displaystyle x_2(t)$ are differentiable and:

$\displaystyle x_1(t_0) \leq x_0, x_1' \leq f(t,x_1), t \geq t_0$
$\displaystyle x_2(t_0) \geq x_0, x_2' \geq f(t,x_2), t \geq t_0$

Show that for $\displaystyle t \geq t_0: x_1(t) \leq x(t) \leq x_2(t)$.
Thank you very much!