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1. Use Laplace transforms to solve the IVP. a. y" - 6y' + 9y = 0; y(0) = −5, y'(0) = −2 b. y" - 9y c. y" - 4y' + 4y = 8t + 2; y(0) = 2, y'(0) = 0 = 10e−2t; y(0) = 0, y'(0) = 4 d. y" + 2y' - 3y = 3 cos 3t; y(0) = 0, y'(0) = e. y" + 36y=-18; y(0) = 3, y'(0) = 6 f. y" + 4y = −4 sint; y(0) = 1, y'(0) = −3 g. y" +2y' + 2y = 10e 2t; y(0) = 4, y'(0) h. y" - 6y' + 5y = 9te²t; y(0) = 0, y'(0) = -3 = 1 = - i. y" 3y4y = 5e4t; y(0) = 2, y'(0) = 3 - - -2 2 j. y" 4y' +13y = 12 sin 3t; y(0) = 0, y'(0) = 0 k. y" 4y = cos 2t; y(0) = 2, y'(0) = −5 + . y' + y = 6t sin t; y(0) = 0

1. Use Laplace transforms to solve the IVP. a. y" - 6y' + 9y = 0; y(0) = −5, y'(0) = −2 b. y" - 9y c. y" - 4y' + 4y = 8t + 2; y(0) = 2, y'(0) = 0 = 10e−2t; y(0) = 0, y'(0) = 4 d. y" + 2y' - 3y = 3 cos 3t; y(0) = 0, y'(0) = e. y" + 36y=-18; y(0) = 3, y'(0) = 6 f. y" + 4y = −4 sint; y(0) = 1, y'(0) = −3 g. y" +2y' + 2y = 10e 2t; y(0) = 4, y'(0) h. y" - 6y' + 5y = 9te²t; y(0) = 0, y'(0) = -3 = 1 = - i. y" 3y4y = 5e4t; y(0) = 2, y'(0) = 3 - - -2 2 j. y" 4y' +13y = 12 sin 3t; y(0) = 0, y'(0) = 0 k. y" 4y = cos 2t; y(0) = 2, y'(0) = −5 + . y' + y = 6t sin t; y(0) = 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Use Laplace transforms to solve the IVP. a. y" - 6y' + 9y = 0; y(0) = −5, y'(0) = −2 b. y" - 9y c. y" - 4y' + 4y = 8t + 2; y(0) = 2, y'(0) = 0 = 10e−2t; y(0) = 0, y'(0) = 4 d. y" + 2y' - 3y = 3 cos 3t; y(0) = 0, y'(0) = e. y" + 36y=-18; y(0) = 3, y'(0) = 6 f. y" + 4y = −4 sint; y(0) = 1, y'(0) = −3 g. y" +2y' + 2y = 10e 2t; y(0) = 4, y'(0) h. y" - 6y' + 5y = 9te²t; y(0) = 0, y'(0) = -3 = 1 = - i. y" 3y4y = 5e4t; y(0) = 2, y'(0) = 3 - - -2 2 j. y" 4y' +13y = 12 sin 3t; y(0) = 0, y'(0) = 0 k. y" 4y = cos 2t; y(0) = 2, y'(0) = −5 + . y' + y = 6t sin t; y(0) = 0
Transcribed Image Text:1. Use Laplace transforms to solve the IVP. a. y" - 6y' + 9y = 0; y(0) = −5, y'(0) = −2 b. y" - 9y c. y" - 4y' + 4y = 8t + 2; y(0) = 2, y'(0) = 0 = 10e−2t; y(0) = 0, y'(0) = 4 d. y" + 2y' - 3y = 3 cos 3t; y(0) = 0, y'(0) = e. y" + 36y=-18; y(0) = 3, y'(0) = 6 f. y" + 4y = −4 sint; y(0) = 1, y'(0) = −3 g. y" +2y' + 2y = 10e 2t; y(0) = 4, y'(0) h. y" - 6y' + 5y = 9te²t; y(0) = 0, y'(0) = -3 = 1 = - i. y" 3y4y = 5e4t; y(0) = 2, y'(0) = 3 - - -2 2 j. y" 4y' +13y = 12 sin 3t; y(0) = 0, y'(0) = 0 k. y" 4y = cos 2t; y(0) = 2, y'(0) = −5 + . y' + y = 6t sin t; y(0) = 0
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