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82. x" +2x' +2x = 3t² et cos 2t + te-¹ sin 2t.

82. x" +2x' +2x = 3t² et cos 2t + te-¹ sin 2t.

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

give the form for xp if the method of undetermined coefficients were to be used. You need not actually compute xp .

**Problem 82.** Solve the differential equation: \[ x'' + 2x' + 2x = 3t^2 e^{-t} \cos 2t + t e^{-t} \sin 2t. \] This is a second-order linear differential equation with variable coefficients involving both exponential and trigonometric terms.
Transcribed Image Text:**Problem 82.** Solve the differential equation: \[ x'' + 2x' + 2x = 3t^2 e^{-t} \cos 2t + t e^{-t} \sin 2t. \] This is a second-order linear differential equation with variable coefficients involving both exponential and trigonometric terms.
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