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+ | | 5. 25 dr dx dt x(0) + W dy dt dy dt - 2x = 1 - 3x - 3y = 2 0, y(0) = 0

+ | | 5. 25 dr dx dt x(0) + W dy dt dy dt - 2x = 1 - 3x - 3y = 2 0, y(0) = 0

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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. 9. dx 1. =-x+y 3. 11. 7. dy dt x(0) = 0, y(0) = 1 dx dt 5. 2 =2r = x - 2y 5x-1 dt x(0) = -1, y(0) = 2 dx dy + dt dt dx dt dy +== -3x - 3y = 2 dt x(0) = 0, y(0) = 0 +x=y=0 di² d'y dr² + y - x = 0 2x x(0) = 0, x'(0) = -2, y(0) = 0, y'(0) = 1 d'x d'y diª d'x + dr d'y di² +3 = 4t x(0) = 8, x'(0) = 0, y(0) = 0, y'(0) = 0 d³x di d²x dy dt = 1 +3y=0 + 3y = te x(0)=0, x'(0) = 2, v(0) = 0 2. 4. 6. 8. 10. 12. dx dt dy dt x(0) = 1, y(0) = 1 dx dr = 2y + e <= 8x-t dx dt dx dt + 3x + x(0) = 0, y(0) = 0 dy dt + X- dx dt dx dt x+ dx dy dt dr x(0) = 0, y(0) = 1 dix dx dy dr²2 dt dt dx dy di dy dt dt dy dt + d'y dy + diª dt x(0) = 1, x'(0) = 0, y(0) = -1, y'(0)=5 y=e 4x + 21 + y = 0 + 2y = 0 2 4 <=0 dt di²³ 0 d'y di x(0) = 0, y(0) = 0. y'(0) = 0, y" (0) = 0 = 6 sin = 0 = 4x - 2y + 2/(1-1 = 3x - y + (1-
Transcribed Image Text: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. 9. dx 1. =-x+y 3. 11. 7. dy dt x(0) = 0, y(0) = 1 dx dt 5. 2 =2r = x - 2y 5x-1 dt x(0) = -1, y(0) = 2 dx dy + dt dt dx dt dy +== -3x - 3y = 2 dt x(0) = 0, y(0) = 0 +x=y=0 di² d'y dr² + y - x = 0 2x x(0) = 0, x'(0) = -2, y(0) = 0, y'(0) = 1 d'x d'y diª d'x + dr d'y di² +3 = 4t x(0) = 8, x'(0) = 0, y(0) = 0, y'(0) = 0 d³x di d²x dy dt = 1 +3y=0 + 3y = te x(0)=0, x'(0) = 2, v(0) = 0 2. 4. 6. 8. 10. 12. dx dt dy dt x(0) = 1, y(0) = 1 dx dr = 2y + e <= 8x-t dx dt dx dt + 3x + x(0) = 0, y(0) = 0 dy dt + X- dx dt dx dt x+ dx dy dt dr x(0) = 0, y(0) = 1 dix dx dy dr²2 dt dt dx dy di dy dt dt dy dt + d'y dy + diª dt x(0) = 1, x'(0) = 0, y(0) = -1, y'(0)=5 y=e 4x + 21 + y = 0 + 2y = 0 2 4 <=0 dt di²³ 0 d'y di x(0) = 0, y(0) = 0. y'(0) = 0, y" (0) = 0 = 6 sin = 0 = 4x - 2y + 2/(1-1 = 3x - y + (1-
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