The purpose of this page is to provide "just enough" documentation of some ODE tools that could be useful when you're looking for differential invariants and ghosts.

Mathematica

All of the typical visualizations are possible in Mathematica, and there's some nice documentation out there (TODO -- provide links to DSolve, vector field w/ solutions, ...). Additionally, the EquationTrekker is a nice tool for exploring particular initial values:

<< EquationTrekker`
EquationTrekker[{x'[t] == v[t], v'[t] == - x[t]}, {x[t], v[t]}, {t, 0, 100}]