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x" +4x'+3x = 5(t – 4), x(0) = 4, x'(0) = 2 Solve the above IVP using Laplace Transforms and then find x(4.2). Put x(4.2) accurately calculated to the nearest thousandth (3 decimal places) in the answer box. Notation: dx -and x = x(t). dt and x' = dt? 5(t) is the Dirac delta function.

x" +4x'+3x = 5(t – 4), x(0) = 4, x'(0) = 2 Solve the above IVP using Laplace Transforms and then find x(4.2). Put x(4.2) accurately calculated to the nearest thousandth (3 decimal places) in the answer box. Notation: dx -and x = x(t). dt and x' = dt? 5(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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please solve the following

[ordinary differential equations; topic] Please solve the following problem Provide a well explained and understandable(readable) Step by step solution solution

Short list of important Laplace transforms. f(t) F(s) | f(t) F(s) (s > a) (8 > 0) s" F(s) – E-1 s"-k f(k-1) (0) F(s – a) n! t" (integer n 2 0) cos kt (s > 0) (s > 0) (s > 0) eat 8-a sin kt u(t – a) da (t) = 6(t – a) (a > 0) eat cos kt f(n) (t) eat f(t) (8 > a) | eat sin kt (n < s) Itu(D-s) Só s(7) dr e-as k=1 eas (s > a) 8-a (メーa)2+2 n! (sーa)2+2 F(s) eat in (integer n > 0) tf(t) u(t – a)f(t – a) F(s) e-as F(s) F(s/a) f(at) (a > 0) x" +4x'+3x S(t – 4), x(0) = 4, x'(0) = 2 - Solve the above IVP using Laplace Transforms and then find x(4.2). Put x(4.2) accurately calculated to the nearest thousandth (3 decimal places) in the answer box. Notation: dx -and x = x(t). dt dex x": and x' = dt? 5(t) is the Dirac delta function.
Transcribed Image Text:Short list of important Laplace transforms. f(t) F(s) | f(t) F(s) (s > a) (8 > 0) s" F(s) – E-1 s"-k f(k-1) (0) F(s – a) n! t" (integer n 2 0) cos kt (s > 0) (s > 0) (s > 0) eat 8-a sin kt u(t – a) da (t) = 6(t – a) (a > 0) eat cos kt f(n) (t) eat f(t) (8 > a) | eat sin kt (n < s) Itu(D-s) Só s(7) dr e-as k=1 eas (s > a) 8-a (メーa)2+2 n! (sーa)2+2 F(s) eat in (integer n > 0) tf(t) u(t – a)f(t – a) F(s) e-as F(s) F(s/a) f(at) (a > 0) x" +4x'+3x S(t – 4), x(0) = 4, x'(0) = 2 - Solve the above IVP using Laplace Transforms and then find x(4.2). Put x(4.2) accurately calculated to the nearest thousandth (3 decimal places) in the answer box. Notation: dx -and x = x(t). dt dex x": and x' = dt? 5(t) is the Dirac delta function.
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