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Solve the given differential equation by undetermined coefficients. y" + 2y'=2x+9-e-2x

Solve the given differential equation by undetermined coefficients. y" + 2y'=2x+9-e-2x

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) = y" +2y'=2x +9-e-2x exp(2x) (C₁ sin(x) + C² cos(x) ) + x²/4 + x exp(-2x)/4 C₁ exp(-2x) + C₂ x exp(-2x) + x³/3 + x² exp(-2x)/2 + x C₁ exp(2x) + C₂ exp(-2x) + x/2 + x exp(-2x) + x² C₁ exp(-2x) + C₂ + x²/2 + x exp(-2x)/2 + 4x C₁ sin(2x) + C₂ cos(2x) + x²/2 + x exp(-2x)/2 + x³ C₁ exp(x) + C₂ exp(-x) + x/6 + 2x exp(-x) 0 No solution
Transcribed Image Text:Solve the given differential equation by undetermined coefficients. y(x) = y" +2y'=2x +9-e-2x exp(2x) (C₁ sin(x) + C² cos(x) ) + x²/4 + x exp(-2x)/4 C₁ exp(-2x) + C₂ x exp(-2x) + x³/3 + x² exp(-2x)/2 + x C₁ exp(2x) + C₂ exp(-2x) + x/2 + x exp(-2x) + x² C₁ exp(-2x) + C₂ + x²/2 + x exp(-2x)/2 + 4x C₁ sin(2x) + C₂ cos(2x) + x²/2 + x exp(-2x)/2 + x³ C₁ exp(x) + C₂ exp(-x) + x/6 + 2x exp(-x) 0 No solution
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