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Use the Laplace transform to solve the given initial-value problem. y(t) = y" - 6y' +9y=t, y(0) = 0, y'(0) = 1 (6/5) t exp(4t) + 2t/5 + (3/25) exp(-t) - 1/25 (10/9) t exp(3t) + t/9 (2/27) exp(3t) + 2/27 (4/3) t exp(-3t) - t/3+ (1/9) exp(-3t) + 1/9 (5/4) t exp(2t) + t/4 + (1/16) exp(2t) (8/7) t exp(-t) + 3t/7 + (2/49) exp(-t) - 1/49 (3/2) t exp(-4t) + 5t/2 + (3/4) exp(-4t) - 1/4 (7/6) t exp(t) - t/6 + (1/36) exp(-t) + 1/36 (9/8) t exp(-2t) + 5t/8+ (1/16) exp(-2t) 0 No solution

Use the Laplace transform to solve the given initial-value problem. y(t) = y" - 6y' +9y=t, y(0) = 0, y'(0) = 1 (6/5) t exp(4t) + 2t/5 + (3/25) exp(-t) - 1/25 (10/9) t exp(3t) + t/9 (2/27) exp(3t) + 2/27 (4/3) t exp(-3t) - t/3+ (1/9) exp(-3t) + 1/9 (5/4) t exp(2t) + t/4 + (1/16) exp(2t) (8/7) t exp(-t) + 3t/7 + (2/49) exp(-t) - 1/49 (3/2) t exp(-4t) + 5t/2 + (3/4) exp(-4t) - 1/4 (7/6) t exp(t) - t/6 + (1/36) exp(-t) + 1/36 (9/8) t exp(-2t) + 5t/8+ (1/16) exp(-2t) 0 No solution

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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Use the Laplace transform to solve the given initial-value problem. y(t) = y" - 6y' +9y=t, y(0) = 0, y'(0) = 1 (6/5) t exp(4t) + 2t/5 + (3/25) exp(-t) - 1/25 (10/9) t exp(3t) + t/9 (2/27) exp(3t) + 2/27 (4/3) t exp(-3t) - t/3 + (1/9) exp(-3t) + 1/9 (5/4) t exp(2t) + t/4+ (1/16) exp(2t) (8/7) t exp(-t) + 3t/7 + (2/49) exp(-t) - 1/49 (3/2) t exp(-4t) + 5t/2 + (3/4) exp(-4t) - 1/4 (7/6) t exp(t)- t/6+ (1/36) exp(-t) + 1/36 (9/8) t exp(-2t) + 5t/8+ (1/16) exp(-2t) 0 No solution
Transcribed Image Text:Use the Laplace transform to solve the given initial-value problem. y(t) = y" - 6y' +9y=t, y(0) = 0, y'(0) = 1 (6/5) t exp(4t) + 2t/5 + (3/25) exp(-t) - 1/25 (10/9) t exp(3t) + t/9 (2/27) exp(3t) + 2/27 (4/3) t exp(-3t) - t/3 + (1/9) exp(-3t) + 1/9 (5/4) t exp(2t) + t/4+ (1/16) exp(2t) (8/7) t exp(-t) + 3t/7 + (2/49) exp(-t) - 1/49 (3/2) t exp(-4t) + 5t/2 + (3/4) exp(-4t) - 1/4 (7/6) t exp(t)- t/6+ (1/36) exp(-t) + 1/36 (9/8) t exp(-2t) + 5t/8+ (1/16) exp(-2t) 0 No solution
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