Say you have to classify nodes when studying the stability of Non-Linear Systems. Use the Differential Equations Made Easy App at www.TinspireApps.com under menu item 3 E . Enter the given System as follows in the two top boxes:
When plugging the critical points into the Jacobian we are able to compute the EigenValues that allow us to classify the nodes as stable, unstable, saddle point, center or spiral point.
and finally
Very Simple!