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x" +3x' + 2x = 5(t – 4), x(0) = 5, x'(0) = 7 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.

x" +3x' + 2x = 5(t – 4), x(0) = 5, x'(0) = 7 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.

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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[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) (s > 0) ε"F's) - Σ-1 F(s – a) (8-a)2+k? t" (integer n > 0) cos kt n+I (s > 0) (s > 0) (s > 0) eat 8-0 sin kt 82. -as u(t – a) da(t) = 6(t – a) (a > 0) eat cos kt f(n) (t) eat f(t) s7ー ーk=1 k f(k-1) (0) eas (s > a) | eat sin kt (s > a) (s > a) 8-a (メーa)2+k2 n! (8-a)n+I F(s) Só f(7) dr f(at) (a > 0) F(s/a) eat in (integer n2 0) tf(t) u(t – a)f(t – a) ds e-as F(s) x" +3x'+2x = 5(t – 4), x(0) = 5, x'(0) = 7 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: d²x and x' = dt? dx and x = dt x" = = x(t). S(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) (s > 0) ε"F's) - Σ-1 F(s – a) (8-a)2+k? t" (integer n > 0) cos kt n+I (s > 0) (s > 0) (s > 0) eat 8-0 sin kt 82. -as u(t – a) da(t) = 6(t – a) (a > 0) eat cos kt f(n) (t) eat f(t) s7ー ーk=1 k f(k-1) (0) eas (s > a) | eat sin kt (s > a) (s > a) 8-a (メーa)2+k2 n! (8-a)n+I F(s) Só f(7) dr f(at) (a > 0) F(s/a) eat in (integer n2 0) tf(t) u(t – a)f(t – a) ds e-as F(s) x" +3x'+2x = 5(t – 4), x(0) = 5, x'(0) = 7 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: d²x and x' = dt? dx and x = dt x" = = x(t). S(t) is the Dirac delta function.
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