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Solve the given differential equation by undetermined coefficients. y"-9y=(x²-4) sin(3x)

Solve the given differential equation by undetermined coefficients. y"-9y=(x²-4) sin(3x)

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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Question
Solve the given differential equation by undetermined coefficients. y(x) = 7 y"-9y=(x²-4) sin(3x) - C₁ cos(3x) + C₂ sin(3x) - x³ exp(3x)/4 + (16/37) exp(3x) - x² exp(9x)/4 C₁ exp(-3x) + C₂ x exp(-3x) – x³ sin(6x)/4 + (32/37) sin(6x) – x² cos(6x)/4 exp(-3x) (C₁ sin(3x) + C₂ cos(3x) ) + x² exp(3x)/16 + (37/64) exp(x) C₁ exp(3x) + C₂ x exp(3x) – x² sin(12x)/2 + (31/39) sin(12x) - x² cos(12x)/2 C₁ Cos(3x) + C₂ sin(3x) - x exp(-x)/4 + (33/37) exp(3x) + x² exp(-9x)/4 exp(3x) (C₁ sin(-3x) + C₂ cos(-3x)) + x exp(3x)/16 + (37/64) x² exp(x) C₁ exp(3x) + C₂ exp(-3x) - x² sin(3x)/18+ (37/162) sin(3x) - x cos(3x)/27 0 QUES No solution
Transcribed Image Text:Solve the given differential equation by undetermined coefficients. y(x) = 7 y"-9y=(x²-4) sin(3x) - C₁ cos(3x) + C₂ sin(3x) - x³ exp(3x)/4 + (16/37) exp(3x) - x² exp(9x)/4 C₁ exp(-3x) + C₂ x exp(-3x) – x³ sin(6x)/4 + (32/37) sin(6x) – x² cos(6x)/4 exp(-3x) (C₁ sin(3x) + C₂ cos(3x) ) + x² exp(3x)/16 + (37/64) exp(x) C₁ exp(3x) + C₂ x exp(3x) – x² sin(12x)/2 + (31/39) sin(12x) - x² cos(12x)/2 C₁ Cos(3x) + C₂ sin(3x) - x exp(-x)/4 + (33/37) exp(3x) + x² exp(-9x)/4 exp(3x) (C₁ sin(-3x) + C₂ cos(-3x)) + x exp(3x)/16 + (37/64) x² exp(x) C₁ exp(3x) + C₂ exp(-3x) - x² sin(3x)/18+ (37/162) sin(3x) - x cos(3x)/27 0 QUES No solution
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