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b) Find -1. e-s ((s+1) e¯¹ s²+4s+6

b) Find -1. e-s ((s+1) e¯¹ s²+4s+6

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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Hello there! please help me solve this! calculus questions. Also, i've provide the appendix for sample equations to refer!

b) Find -1. TTS (s+1) e¯ns s²+4s+6
Transcribed Image Text:b) Find -1. TTS (s+1) e¯ns s²+4s+6
Function a (constant) f t" sin at cos at sinh at cosh at eat f(t) f(t-a)u(t-a) t" f(t) f(n) (t) f(u) du f(u)g(t-u) du Trigonometric Identities: APPENDIX TABLE OF LAPLACE TRANSFORMS Laplace Transforms a S 1 s-a n! 50+1 a s² + a² S + a 2 a s²-a² S 2 s² - a² 2 F(s-a) e-as F(s) (-1)"F(")(s) s"F(s)-sn-1f(0)-sn-2f (¹) (0) -- F(s) S F(s) G(s) 2sinAcosB = sin (A + B) + sin (A - B) 2cosAcosB = cos (A - B) + cos (A + B) 2sinAsinB = cos (A-B)- cos (A + B) -f(n-1) (0) sin 2A = 2 sin A cos A cos 2A = cos²A - sin³A = 2 cos²A-1 = 1-2 sin²A sin (A + B) = sin A cos B ± cos A sin B sin A sin B cos (A + B) = cos A cos B cosh?A – sinh?A = 1 sinh (A + B) = sinh A cosh B + cosh A sinh B cosh (A + B) = cosh A cosh B+ sinh A sinh B
Transcribed Image Text:Function a (constant) f t" sin at cos at sinh at cosh at eat f(t) f(t-a)u(t-a) t" f(t) f(n) (t) f(u) du f(u)g(t-u) du Trigonometric Identities: APPENDIX TABLE OF LAPLACE TRANSFORMS Laplace Transforms a S 1 s-a n! 50+1 a s² + a² S + a 2 a s²-a² S 2 s² - a² 2 F(s-a) e-as F(s) (-1)"F(")(s) s"F(s)-sn-1f(0)-sn-2f (¹) (0) -- F(s) S F(s) G(s) 2sinAcosB = sin (A + B) + sin (A - B) 2cosAcosB = cos (A - B) + cos (A + B) 2sinAsinB = cos (A-B)- cos (A + B) -f(n-1) (0) sin 2A = 2 sin A cos A cos 2A = cos²A - sin³A = 2 cos²A-1 = 1-2 sin²A sin (A + B) = sin A cos B ± cos A sin B sin A sin B cos (A + B) = cos A cos B cosh?A – sinh?A = 1 sinh (A + B) = sinh A cosh B + cosh A sinh B cosh (A + B) = cosh A cosh B+ sinh A sinh B
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