2302-practice-mid3 - MAP 2302 Fall 2010 Midterm 3 Review...

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MAP 2302, Fall 2010 — Midterm 3 Review Problems 1 The exam will cover sections 7.2, 7.3, 7.4, 7.5, 7.6, and 7.8. All topics from this review sheet or from the suggested exercises are fair game. 1 Solve for L { y } given the following initial value problems. a. y ′′ - 4 y + 8 y = e 2 t cos 3 t ; y (0) = 1; y (0) = 3. b. y ′′ + 2 y - 3 y = e t + t + 1; y (0) = 9; y (0) = - 3. c. y ′′ - 4 y = braceleftbigg sin t 0 < t < π, - sin t t > π. ; y (0) = y (0) = 0. d. y ′′ + y - 2 y = f ( t ), where f ( t ) is the half-rectified sine wave below; y (0) = y (0) = 1. π 2 π 3 π 4 π 5 π 6 π 1 - 1 e. y ′′ + y - 2 y = f ( t ), where f ( t ) is the sawtooth function below; y (0) = y (0) = 0. 1 2 3 4 5 6 1 - 1 f. y ′′ - 4 y + ty = 0; y (0) = 1; y (0) = 0. (Find a differential equation satisfied by L { y } .) g. y ′′ + 4 y
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