Problem 2 Consider an autonomous system of differential equations
where is a vector field.
- Let and be two solutions on . Assuming that
for all x, z in , show that is a decreasing function of .
- 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.