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x" + 3x'+ 2x = 5(t – 4), x(0) = 8, x'(0) = 6 Solve the above IVP using Laplace Transforms and then find x(4.1). Put x(4.1) accurately calculated to the nearest thousandth (3 decimal places) in the answer box. Notation: d?x and x' = dt? dx and x= x(t). dt x" = S(t) is the Dirac delta function.

x" + 3x'+ 2x = 5(t – 4), x(0) = 8, x'(0) = 6 Solve the above IVP using Laplace Transforms and then find x(4.1). Put x(4.1) accurately calculated to the nearest thousandth (3 decimal places) in the answer box. Notation: d?x and x' = dt? dx and x= x(t). dt x" = S(t) is the Dirac delta function.

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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Answer to 3 decimal places please 

QUESTION 7 12 points Save Answer Short list of important Laplace transforms. f(t) F(8) | f(t) F(s) g (s > a) (8 > 0) s"F(s) -Σ-1 F(s — а) n! t" (integer n >0) cos kt (8 > 0) (s > 0) (8 > 0) eat sin kt f(n) (t) eat f(t) eat sin kt f(k-1) (0) e-as u(t – a) da(t) = 8(t – a) (a >0) eat cos kt sn-k 8 e-as (s > a) (s > a) (s > a) 8-a (8-a)²+k² n! (8-a)n+I Só F(7) dr f(at) (a > 0) s-a)2+k2 F(s) eat in (integer n> 0) -F(s) F(s/a) tf(t) и(t — а)f(t — а) e-as F(s) х"+ 3x'+ 2х3 5(t — 4), х(0) 3D 8, х'(0) 3D 6 Solve the above IVP using Laplace Transforms and then find x(4.1). Put x(4.1) accurately calculated to the nearest thousandth (3 decimal places) in the answer box. Notation: dx and x = x(t). dt x" = and x' = dt? S(t) is the Dirac delta function.
Transcribed Image Text:QUESTION 7 12 points Save Answer Short list of important Laplace transforms. f(t) F(8) | f(t) F(s) g (s > a) (8 > 0) s"F(s) -Σ-1 F(s — а) n! t" (integer n >0) cos kt (8 > 0) (s > 0) (8 > 0) eat sin kt f(n) (t) eat f(t) eat sin kt f(k-1) (0) e-as u(t – a) da(t) = 8(t – a) (a >0) eat cos kt sn-k 8 e-as (s > a) (s > a) (s > a) 8-a (8-a)²+k² n! (8-a)n+I Só F(7) dr f(at) (a > 0) s-a)2+k2 F(s) eat in (integer n> 0) -F(s) F(s/a) tf(t) и(t — а)f(t — а) e-as F(s) х"+ 3x'+ 2х3 5(t — 4), х(0) 3D 8, х'(0) 3D 6 Solve the above IVP using Laplace Transforms and then find x(4.1). Put x(4.1) accurately calculated to the nearest thousandth (3 decimal places) in the answer box. Notation: dx and x = x(t). dt x" = and x' = dt? S(t) is the Dirac delta function.
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