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2302-practice-mid2

# 2302-practice-mid2 - a y ′′-4 y ′-21 y = 2 e 7 t b y...

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MAP 2302, Fall 2010 — Midterm 2 Review Problems 1 The exam will cover sections 4.2, 4.3, 4.4, 4.5, and 4.6. All topics from this review sheet or from the suggested exercises are fair game. 1 Solve the following initial value problems. a. y ′′ - 4 y + 8 y = 0; y (0) = 1; y (0) = 0. b. y ′′ + 2 y - 3 y = 0; y (0) = 9; y (0) = - 3. c. y ′′ - 4 y = 0; y (0) = 2; y (0) = - 98. 2 What form of particular solution y p would you guess in order to solve the following differential equations using the method of undetermined coefficients? Do not solve these problems.
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Unformatted text preview: a. y ′′-4 y ′-21 y = 2 e 7 t . b. y ′′-2 y ′-8 y = 19 t cos(2 t ). c. y ′′-4 y ′ + 5 y = 7 e 2 t sin t + t . 3 Solve the following diFerential equations. b. y ′′ + 4 y = tan 2 t . c. y ′′′-2 y ′′ + 17 y ′ = e 3 t . e. y ′′-4 y ′ + 4 y = te 2 t . 4 Solve the following initial value problems. a. y ′′-9 y = 18 t ; y (0) = 1; y ′ (0) = 11. b. y ′′-y ′-2 y = 2 e − t + 4; y (0) = 10; y ′ (0) =-3....
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