(a) Given the non-homogeneous differential equation y" + 2y + 5y = f(t), provide the form of yp for the following expressions for f(t). You need not determine values of unknown coefficients. i. f(t) = 2t³ - 3t ii. f(t) = 2 sint (b) Given the nonhomogeneous differential equation y" - 6y' +9y = f(t), provide the form of yp for the following expressions for f(t). You need not determine values of unknown coefficients. i. f(t) = et + sint iii. f(t) = tet ii. f(t) = te³t
(a) Given the non-homogeneous differential equation y" + 2y + 5y = f(t), provide the form of yp for the following expressions for f(t). You need not determine values of unknown coefficients. i. f(t) = 2t³ - 3t ii. f(t) = 2 sint (b) Given the nonhomogeneous differential equation y" - 6y' +9y = f(t), provide the form of yp for the following expressions for f(t). You need not determine values of unknown coefficients. i. f(t) = et + sint iii. f(t) = tet ii. f(t) = te³t
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:2. Undetermined Coefficients:
(a) Given the non-homogeneous differential equation
y" + 2y' + 5y = f(t),
provide the form of yp for the following expressions for f(t). You need not determine values of unknown
coefficients.
i. f(t) = 2t³ . 3t
ii. f(t) = 2 sint
(b) Given the nonhomogeneous differential equation
y" - 6y' +9y = f(t),
provide the form of yp for the following expressions for f(t). You need not determine values of unknown
coefficients.
i. f(t) = e-t + sint
е
iii. f(t) = tet
ii. f(t) = te³t
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