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In Problems 13-15, find a particular solution using the "definite integral" form of Variation of Parameters. This formula reads Up(t) = f* g(t = T)q(T) dT, where the form of the growth factor depends on the roots of the characteristic equation: e³2(t-T) - e$1(t-T) 82-81 g(t-T)=(t-T)es(t-T), ea(t-T)5 13. y" + 3y + 2y = e-t. sin(w(t-T)) لیا distinct roots 81, 82, repeated root 8, s = a ±iw.

In Problems 13-15, find a particular solution using the "definite integral" form of Variation of Parameters. This formula reads Up(t) = f* g(t = T)q(T) dT, where the form of the growth factor depends on the roots of the characteristic equation: e³2(t-T) - e$1(t-T) 82-81 g(t-T)=(t-T)es(t-T), ea(t-T)5 13. y" + 3y + 2y = e-t. sin(w(t-T)) لیا distinct roots 81, 82, repeated root 8, s = a ±iw.

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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In Problems 13-15, find a particular solution using the "definite integral" form of Variation of Parameters. This formula reads Up(t) = f* g(t = T)q(T) dT, where the form of the growth factor depends on the roots of the characteristic equation: e³2(t-T) - e$1(t-T) 82-81 g(t-T)=(t-T)e*(t-T), ea(t-T) 13. y" + 3y + 2y = e-t. 14. y" + 2y15y = 3H(t-2). 15. y" - 2y + 5y = 26 (t-3). sin(w(t-T)) لیا distinct roots 81, 82, repeated root s, s = a ±iw.
Transcribed Image Text:In Problems 13-15, find a particular solution using the "definite integral" form of Variation of Parameters. This formula reads Up(t) = f* g(t = T)q(T) dT, where the form of the growth factor depends on the roots of the characteristic equation: e³2(t-T) - e$1(t-T) 82-81 g(t-T)=(t-T)e*(t-T), ea(t-T) 13. y" + 3y + 2y = e-t. 14. y" + 2y15y = 3H(t-2). 15. y" - 2y + 5y = 26 (t-3). sin(w(t-T)) لیا distinct roots 81, 82, repeated root s, s = a ±iw.
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