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Unformatted text preview: Answer: using , , so we need and for both and to exist. The plane region is given by and or and . 5. (18 pts.) Consider the differential equation . 1. Determine and classify the equilibrium (critical) points for the equation. Answer: when and ; . and , so is unstable and is stable. 2. Determine the solution for the equation if y(0) = 2. Answer: , so separable . Now , so , and , or . Using , . Final solution: ; 6. (10 pts.) Solve the differential equation , with . Answer: , so linear with . Then , , and . Using , . Final solution: . 7. (15 pts.) Consider the differential equation . 1. Find the general solution for the equation. Answer: The characteristic equation is , so or ; general solution is . 2. Determine the Wronskian for fundamental solution set. Answer: . 3. Determine the solution that satisfies initial conditions , . Answer: and , so and , . Final solution: ....
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 Spring '08
 GOLDBERG
 Math, Differential Equations, Equations, Complex number, 10 pts, 15 pts, 7 pts

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