# Math Help - Why ode solution tends to a constant?

1. ## Why ode solution tends to a constant?

Problem 2 Consider an autonomous system of differential equations

where is a vector field.
1. Let and be two solutions on . Assuming that

for all x, z in , show that is a decreasing function of .
2. Let be a solution defined for . Assuming that

show that there exists such that

Would someone help me in the second question? I have no idea about it.

PS: This is Berkely math problem Fall 81, Problem 2.