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Determine the form of a particular solution to the differential equations. Do not solve. (a) x" – x' – 2x = e' cos t – t² + cos 3t - - - (b) y" – y' + 2y = (2x + 1)ež cos r + 3(x³ – x)ež sin x - -

Determine the form of a particular solution to the differential equations. Do not solve. (a) x" – x' – 2x = e' cos t – t² + cos 3t - - - (b) y" – y' + 2y = (2x + 1)ež cos r + 3(x³ – x)ež sin x - -

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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2. Determine the form of a particular solution to the differential equations. Do not solve. (a) \( x'' - x' - 2x = e^t \cos t - t^2 + \cos 3t \) (b) \( y'' - y' + 2y = (2x + 1)e^{\frac{x}{2}} \cos \frac{\sqrt{7}}{2} x + 3(x^3 - x)e^{\frac{x}{2}} \sin \frac{\sqrt{7}}{2} x \)
Transcribed Image Text:2. Determine the form of a particular solution to the differential equations. Do not solve. (a) \( x'' - x' - 2x = e^t \cos t - t^2 + \cos 3t \) (b) \( y'' - y' + 2y = (2x + 1)e^{\frac{x}{2}} \cos \frac{\sqrt{7}}{2} x + 3(x^3 - x)e^{\frac{x}{2}} \sin \frac{\sqrt{7}}{2} x \)
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