(a) Consider y" – 3y' – 2y = te-t sin(3t) – 4e-t +5t2 – 2. Write down the most efficient “guess" for a particular solution as suggested by the method of undetermined coefficients. Don't worry about determining the coefficients and actually solving. Just write down the "form" for the particular solution.
(a) Consider y" – 3y' – 2y = te-t sin(3t) – 4e-t +5t2 – 2. Write down the most efficient “guess" for a particular solution as suggested by the method of undetermined coefficients. Don't worry about determining the coefficients and actually solving. Just write down the "form" for the particular solution.
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:Non-Homogeneous Problems: You might want to use software to help differentiate, determine undeter-
mined coefficients (i.e., solve equations), and factor characteristic polynomials.
(a) Consider y" – 3y' – 2y = te¬t sin(3t) – 4e-t+5t² – 2. Write down the most efficient "guess" for a
solution as suggested by the method of undetermined coefficients.
Don't worry about determining the coefficients and actually solving. Just write down the "form" for the
particular solution.
יי
particular
(b) Solve ty" + ty' + 4y :
(c) Solve y" – 4y' + 3y = t³ + 3 using (1) the method of undetermined coefficients and (2) variation of
sin(ln(t2)) + 3/t using the method of undetermined coefficients.
=
parameters.
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