# 3d phase space-surface

by marellasunny
Tags: differentialeqs, phase space
The solution of a 3D (ordinary) differential equation is a function from the reals to $\mathbb{R}^3$, in other words a curve (or a fixed point). If there is a conserved quantity, then the solution curve must lie on a surface on which that quantity is constant, but it's still a curve.