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1. 3. dr dt x(0)-0, y(0) - 1 --x-2y dx dt dy <= 2x 1 = 5x - y x(0)=-1. y(0) = 2 dt

1. 3. dr dt x(0)-0, y(0) - 1 --x-2y dx dt dy <= 2x 1 = 5x - y x(0)=-1. y(0) = 2 dt

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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9. EXERCISES 8.2 Answers to odd-numbered problems begin on page A-18. In Problems 1-12 use the Laplace transform to solve the given system of t ferential equations. dx 1. --x+y dr 11. 3. 7. dy dt x(0) = 0, y(0) = 1 dx dt = 2r =x-2y 51- dt x(0) = -1. y(0) = 2 dy dt 5. 2 + dt dx dt d'y df² x(0) = 0. y(0) = 0 d²x +x=y=0 di² dy +-3x - 3y = 2 dt + y - x = 0 2x x(0) = 0.x'(0) = -2, y(0) = 0, y'(0) = 1 d'x d'y + di² di d'x d'y di² +3 = 4t dy dt x(0) = 8, x'(0) = 0, y(0) = 0, y'(0) = 0 dix di d²x di² + 3y = tet x(0)=0, x'(0) = 2, v(0) = 0 = 1 +3y=0 2. 4. 6. 8. 10. 12. dx dt dy dt x(0) = 1, y(0) = 1 dx dr dx dt = 2y + e dx di <= 8x-t + 3x + dx dt x(0) = 0, y(0) = 0 dy dt +x- dx dt dx dt dy dt x(0) = 0, y(0) = 1 d²x dx dy di² dt dt d'y dy + drª dt X+ dx dt dy dy di dt dy dt + 2x x(0) = 1, x'(0) = 0, y(0) = -1, y'(0) 5 = + 4x + y=e + y = 0 21 + 2y = 0 2 =0 dx 4 <=0 dt di³ x(0) = 0, y(0) = 0. y'(0) = 0, y" (0) = 0 di = 6 sin! = 0 = 4x - 2y + 2(1-1 3x - y + (1-
Transcribed Image Text:9. EXERCISES 8.2 Answers to odd-numbered problems begin on page A-18. In Problems 1-12 use the Laplace transform to solve the given system of t ferential equations. dx 1. --x+y dr 11. 3. 7. dy dt x(0) = 0, y(0) = 1 dx dt = 2r =x-2y 51- dt x(0) = -1. y(0) = 2 dy dt 5. 2 + dt dx dt d'y df² x(0) = 0. y(0) = 0 d²x +x=y=0 di² dy +-3x - 3y = 2 dt + y - x = 0 2x x(0) = 0.x'(0) = -2, y(0) = 0, y'(0) = 1 d'x d'y + di² di d'x d'y di² +3 = 4t dy dt x(0) = 8, x'(0) = 0, y(0) = 0, y'(0) = 0 dix di d²x di² + 3y = tet x(0)=0, x'(0) = 2, v(0) = 0 = 1 +3y=0 2. 4. 6. 8. 10. 12. dx dt dy dt x(0) = 1, y(0) = 1 dx dr dx dt = 2y + e dx di <= 8x-t + 3x + dx dt x(0) = 0, y(0) = 0 dy dt +x- dx dt dx dt dy dt x(0) = 0, y(0) = 1 d²x dx dy di² dt dt d'y dy + drª dt X+ dx dt dy dy di dt dy dt + 2x x(0) = 1, x'(0) = 0, y(0) = -1, y'(0) 5 = + 4x + y=e + y = 0 21 + 2y = 0 2 =0 dx 4 <=0 dt di³ x(0) = 0, y(0) = 0. y'(0) = 0, y" (0) = 0 di = 6 sin! = 0 = 4x - 2y + 2(1-1 3x - y + (1-
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