quiz7 - Math 250a(Kennedy Quiz 7 Fall ’07 1 Consider the...

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Unformatted text preview: Math 250a (Kennedy) - Quiz 7 - Fall ’07 1. Consider the differential equation: 3/ = (y — 5)(y — a), where a is a parameter with no restrictions. Clearly y = 5 and y = a are equilibrium solutions. Determine when each is stable, unstable and semistable. You can give your answer in the form of sentences or a bifurcation diagram. 20)} 2 (9V5) (9“4/ 2 92 ~S‘2 ~ «9» Tfa 2. Let y(:c) be the solution of y’ = x/y with the initial condition y(1) = 2. For each of the following show your work and reasoning. You can use the slope field to check your answer, but correct answers only get no points. (a) Determine if y is increasing or decreasing at w = 1 and explain why. Y thl); ’7“: >0 / f0 [jg (AQrEuIn-{j‘ (b) Determine if y is concave up or down at x = 1 and explain why. u F “51'"m2‘ fl 9—“? 9 ’ ”\f’ ’ ‘7 y’- L\ p. '1 54 c? (H52 2 2 >0 ...
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