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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.

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.FOM: Focus On Modeling: Vectors Fields
Problem 18P
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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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