Solve the given differential equation by undetermined coefficients. y"+2y=-18x²2x
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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Transcribed Image Text:Solve the given differential equation by undetermined coefficients.
y(x) =
y" + 2y = -18x²2x
exp(x) (C₁ cos(√3 x) + C² sin(√3 x)) + −4x² + 3x − 2
C₁ sin(√2 x) + C₂ cos(√2 x) + exp(2x) (−3x² + 4x − 5/3)
exp(-x) (C₁ sin(√2 x) + C₂ cos(√2 x)) + exp(2x) (2x² - 5x + 4/3)
C₁ exp(2x) + C₂ x exp(2x) + exp(-2x) ( −2x³ + 5x² – 3x/4)
C₁ sin(x/2) + C₂ cos(x/2) - exp(2x) ( 3x² + 2x - 3/5)
C₁ exp(2x) + C₂ exp(-2x) + exp(x) (2x² + 3x - 1/3)
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