0 Spring 2016 261 Review for Test 2

0 Spring 2016 261 Review for Test 2 - Math 261 Review for...

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Math 261 Review for Test2 PART I The Wronskian: how to evaluate; how to use to prove linear independence of the given set of functions. Linear Homogeneous Equation: a fundamental set of solutions, the general solution. How to solve Homogeneous Equations with constant coefficients. Reduction of Order Nonhomogeneous Equations: Method of Undetermined Coefficients, Variations of Pa- rameters. Mechanical Vibration: undamped free vibrations, damped free vibrations. Series Solution near an ordinary point PART II 1. Find the Wronskian of the set { sin(3 x ) , cos(3 x ) , 1 } . Is this set linerly independent? 2. Is the set { 1 , x, x 3 } a fundamental set of solutions for the differential equation xy 000 - y 00 = 0? 3. y 00 - 2 y 0 + y = 0. Is the general solution y = c 1 e x + c 2 xe x ? 4. Solve the following homogeneous equations with constant coefficients: (a) y 00 + 10 y 0 + 21 y = 0 (b) y 00 - 6 y 0 + 9 y = 0 (c) y 00 + 4 y 0 + 5 y = 0 (d) y (4) - y 00 + 20 y = 0 (e) y (4) + y 000 = 0 1
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5. Use the method of reduction of order to find a second solution of the differential equation t
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