GSW Problem Set 2

GSW Problem Set 2 - (c) Suppose y (0) = / 2 . Determine lim...

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EA4 Workshop questions set 2 - week of 10/06/08 1. Consider the equation y 0 = y ( A - y 2 ) (1) where A is a parameter. (a) For every value of A ±nd all critical points of (1). (b) For all values of A determine whether the critical point is stable or unstable. 2. Consider the problem y 0 = f ( y ) = cos y, y (0) = π. (2) Determine lim t →∞ y ( t ) . 3. Consider the equation y 0 = sin y. (3) (a) Find all critical points. (b) Determine the stability of all critical points.
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Unformatted text preview: (c) Suppose y (0) = / 2 . Determine lim t y ( t ) . 4. Give an example of an autonomous equation that has no critical points. Explain what to expect from the solution. 5. Is it possible for the solution to such a problem to have a horizontal asymptote? 6. Find the solution to the problem. y + e x 2 y = y sin x, y (0) = 0 . (4)...
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This note was uploaded on 09/08/2010 for the course GEN_ENG 205 taught by Professor Taflove during the Spring '08 term at Northwestern.

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