Find the Inverse Laplace transforms of the following functions: (4s + 2)/(s2 +6s + 34)1/ [(s-2)(s-4)(s-8)]Subject : DIFFERENTIAL EQUATIONTopic: Inverse Laplace TransformsBelow is the Table of Laplace Transforms. 1.3.5.7.9.f(t)=2²¹{F(s)}119.t", n=1,2,3,...11. sin(at)-at cos(at)21.√tsin(at)t sin (at)13. cos(at)-at sin (at)15. sin(at+b)17. sinh(ar)et sin (br)e” sinh(br)23. te, n=1,2,3,...u(t)= u(t-c)Heaviside Function25.27. u(t)f(t-c)29. eºf(t)31. ƒ(1)33. ff(t-1)g(1) dr35. f'(t)37. f(t)Table of Laplace TransformsF(s) = {f(t)}SLsu+1as² + a²2as(s² + a²)²2a³(s² + a²)²³s(s²_a²)(s² + a²)²s sin (b) + acos (b)s² + a²3²-d²b(s-a)² + b²b(s-a)²-B²n!(s-a)***Se¯ F (s)F(s-c)*F(u) du2.f(t)=2²¹{F(s)}at4. tº,p>-1e6., n=1,2,3,...8. cos(at)10. tcos(at)20.12. sin (at) + at cos(at)22.14. cos(at)+ at sin(at)16. cos(at+b)18.cosh (at)e cos (bt)ea cosh (br)24. f(ct)8(t-c)Dirac Delta Functionu. (t)g(t)26.28.30. tf(t), n=1,2,3,...32. ff(v) dvF(s) G(s)SF (s)-f(0) 36. f(t)34. f(t+T)=f(t)F(s) = £{f(t)}1s-a[(p+1)Sit1-3-5---(2n-1)√√2" 5"Ss² + a²s²-a²(s² + a²)²2as²(s² + a²)²s(s²+3a²)(s² + a²)²scos (b)-a sin (b)s² + a²S3-0²s-a(s-a)² + b²s-a(s-a)²³-5²e{g(t+c)}(-1)" F(") (s)F(s)Sfe" f (t) dt1-es²F (s)-sf (0)-f(0)s"F(s)-5-¹ƒ (0)-5-²ƒ' (0)---sf("~²) (0) — ƒ(¹)(0)- Table Notes1. This list is not a complete listing of Laplace transforms and only contains some ofthe more commonly used Laplace transforms and formulas.2. Recall the definition of hyperbolic functions.e' + ecosh (2sinh3. Be careful when using "normal" trig function vs. hyperbolic functions. The onlydifference in the formulas is the "+ a²" for the "normal" trig functions becomes a"- a*** for the hyperbolic functions!4. Formula #4 uses the Gamma function which is defined asr(t)=x²²dxIf n is a positive integer then,T(n+1)=n!The Gamma function is an extension of the normal factorial function. Here are acouple of quick facts for the Gamma functionI(p+1)=pr (p)p(p+1)(p+2).(p+n−1)=-(2)=√I(p+n)I(p)

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Answered: Find the Inverse Laplace transforms of…

Find the Inverse Laplace transforms of the following functions: (4s + 2)/(s2 +6s + 34) 1/ [(s-2)(s-4)(s-8)]

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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