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I just realized something: For this problem and the other one Asdf posted, the solution, using Laplace Transforms, can be obtained in three easy steps in Mathematica:
I find that amazing! Granted, in general, I'd have to include two extra lines to first calculate the transform and this doesn't help one learn the math; I would not recommend this to anyone just learning the technique, but once learned, this provides an effective, concise means of approching the global behavior of these systems.
Code:
alist = {u, v} /.
Solve[{s u == 2 u - 4 v + 5/s, s v - 1 == - u + 2 v - 3/s}, {u, v}]
x = InverseLaplaceTransform[alist[[1, 1]], s, t]
y = InverseLaplaceTransform[alist[[1, 2]], s, t]I find that amazing! Granted, in general, I'd have to include two extra lines to first calculate the transform and this doesn't help one learn the math; I would not recommend this to anyone just learning the technique, but once learned, this provides an effective, concise means of approching the global behavior of these systems.