MTH 286 Midterm: MTH 286 Cleveland State Test1s02

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15 Feb 2019
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Write your name on the back of your test. 1. (10) use the guess and test method to solve the second order di erential equation initial value problem: d2y dt2 + 6 dy dt. + 8y = 0, y(0) = 2, y (0) = 1. 2. (10) solve the given initial value problem. dy dt t2 y + t3y y(0) = 2. Identify the equilibrium points as sinks, sources or nodes. 4. (15) solve the partially decoupled system dx dt dy dt. 5. (45) consider the pair of systems: (a) dx dt = 3x + 2xy (b) dx dt = 5x x2. 3xy dy dt = 5y + 3xy dy dt = 8y 3xy 3y2 x(t) and y(t) represent population of two di erent species. One system describes a competitive system in which both species are harmed by interaction, for example, cars and pedestrians.

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