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

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

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