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Unformatted text preview: Review problems: Math 527, Exam 2 Problems 1–6 are from last year’s second midterm exam; problem 7 is additional. 1. Consider the system x ′ = 1 − xy , y ′ = x − y 3 . Determine its singular (equilibrium) points and classify each, insofar as possible, using linearization. In particular, classify each equilibrium point as stable or not stable. For each equilibrium point, determine in addition if it is a focus, node, or saddle, if you have the information to do so. If one cannot determine the type from the linearization, say so, and indicate, if possible, the alternatives. No sketch is required. 2. Consider the linear system parenleftbigg x ′ y ′ parenrightbigg = bracketleftbigg − 4 4 1 − 4 bracketrightbiggparenleftbigg x y parenrightbigg . If A is the matrix of coefficients, det( A − λI ) = ( λ + 2)( λ + 6). Classify the singular point at the origin. (Is it stable or unstable, a focus, node, saddle, etc.?) Sketch the phase portrait near the origin. The sketch can be rough but it should have the rightSketch the phase portrait near the origin....
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This note was uploaded on 09/29/2009 for the course 642 527 taught by Professor Speer during the Fall '07 term at Rutgers.
- Fall '07