Ordinary dichotomy and global linearization

Suppose that f(t,x)≤ψ(t)f(t,x)≤ψ(t), ∫−∞+∞ψ(t)dt<+∞,|f(t,x1)−f(t,x2)|≤r(t)|x1−x2||f(t,x1)−f(t,x2)|≤r(t)|x1−x2|, ∫−∞+∞r(t)dt