I have this question and I don't know how to answer it, at all.

x''+x=0 can be solved in two steps which involves solving the equations (dx/dz)^2 + x^2 = c^2

The former equation have unique solutions whereas the latter does not. How do you reconcile these two statements? Does every solution of the latter satisfy the former?

This chapter is dealing with autonomous systems of which I know nothing about..