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Exam 2 - Fall 2003

# Exam 2 - Fall 2003 - Differential Equations Exam#2 Fall...

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Differential Equations Exam #2 Fall 2003 Name_________________________________ Show all your work neatly and in numerical order on notebook paper. You must omit one problem by clearly writing “OMIT” by the problem on your notebook paper. If you do not omit a problem, I will omit the last one for you. DO NOT WRITE ON THE BACKS OF YOUR PAGES. 1. a. Define “fundamental set of solutions”. Be very precise. b. We know that a fundamental set of solutions exists for what type of differential equations? What does this type of differential equation look like? 2. For the differential equation ( 29 x x y y 2 sin 3 4 2 - = + , x c x c y c 2 sin 2 cos 2 1 + = . Find the assumed form of the particular solution p y when using undetermined coefficients. (Do not find p y .) 3. Suppose 1 1 - = m is a root of multiplicity 3 and i m i m 2 1 , 2 1 3 2 - = + = are each roots of multiplicity 1 of an auxiliary equation. Write down the general solution of the corresponding homogeneous linear DE if it is a Cauchy- Euler equation. 4. Solve: 0 16 8 = + + y y y . 5. Solve: 0 2 3 2 = - - y y x y x 6. When solving x e y y y 4 12 = - -
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