First Sentence:
In many (in fact, most) cases, differential equations of the form x' = f(t, x) are inadequate for the description of a physical system; more variables are needed to specify its state at any time t.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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homoclinic saddle connection, heteroclinic saddle connection, repelling limit cycles, stable separatrix, degenerate possibility, differentiable conjugacy, unstable separatrices, saddle connections, weak sink, spiral sink, phase plane behavior, bifurcation locus, essential size, linear sink, distinct absolute values, exceptional trajectory, many limit cycles, spiral source, linearization matrix, upper fence, node sink, two limit cycles, exceptional solution, associated homogeneous equation, degenerate bifurcations
Key Phrases - Capitalized Phrases (CAPs):
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Selected Problems, Implicit Function Theorem, Spectral Theorem, Exercises Exercises, Consider Example, Higher Order Equations, Kepler's First Law, Planar Systems, Repeat Exercise, Asymptotic Development, Bifurcations of Vector Fields, Inverse Function Theorem, Schwarz Inequality
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