x' (t) + 4x' (t) = −2t – sin(t – 4), with x(4) = 0, and x'(4) = 1.

Q: Use the tables of Laplace Transforms to find the inverse Laplace Transform : F(s)= 2 s² +35-4

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: Use the tables of Laplace Transforms to find the inverse Laplace Transform: F(s)=|-e

A: Given Laplace transform is Fs=1-e-2ss2

Q: Show the complete solution for these 2 question:

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Q: 1 а. s2+2s+10

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Q: 1. Problem Solving. Solve the following problems completely. Use additional short coupon bond for…

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Q: L {sin(wt + O)}; w and O are constants

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Q: - f(t) = teat sin bt

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Q: 1 с. s2+7s

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Q: Exercise 6.1.10: Find the inverse Laplace transform of 251

A: We have to find the inverse Laplace transformation of the given function.

Q: Find the inverse Laplace transform of F( where 1 F(s) = s(s? + 2s + 2) %3D

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Q: Exercise 6.1.14: Find the Laplace transform of sin(w(t – a)).

A: We have to find the Laplace transformation of the given function

Q: . Determine the following values for the Laplace transform

A: Determine the following values for the Laplace transform

Q: 2 5. f(t) = e-²t (t³ + 1)²

A: Some of the formulas of Laplace transformation . Ltn=n!sn+1Leat=1s-aLeatf(t)=F(s-a), L[f(t)]=F(s)

Q: s2 + 6s + 8 G(s) = s4 + 8s2 + 16° xnlanation calculation IS we

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Q: 2. Write the program to find Laplace inverse for this equation: 4 s+ 5 Y(s) =& - 4)°(s+5)l %3D

A: The linearity property of Laplace transformation is,  L-1a·fs+b·gs=a·L-1fs+b·L-1gs And,  L-11s-a=eat

Q: This is a two-part question. (a) The correct form for the partial fraction decomposition of 4+5+45…

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Q: L-1(1/(s4+4))

A: L-1s+1s+12+1=e-tcost L-11s+12+1=e-tsint L-1s-1s-12+1=etcost L-11s-12+1=etsint

Q: Solve for the Laplace transform. -2 (sin4 + cosh4t) e¯

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Q: 1+2s s² +4s+7) L 얍

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Q: Solve the following problem and show your complete solutions. Explain your answers for better…

A: Let the laplace transform of g(t) be G(s),That is L{g(t)}=G(s)Then the laplace transform of…

Q: 1 ++²)

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Q: 1. Solve for the inverse Laplace of the functions below.

A: We use inverse Laplace Transform for the given function.

Q: 5: Find the Laplace transform of 3 + t5 + sin(πt).

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Q: Solve the following Laplace Transform of Algebraic Expression: 5. Finf the L t?e-3t ? Show Solution.

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Q: (b) Sketch the following function. Write down its equation in unit step function and find its…

A: Given

Q: = f(t) = t6 — 4t² +5 -

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Q: Use the tables of Laplace Transforms to find the inverse Laplace Transform: F(s)= 2(s-De?S s²-25+2…

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Q: 4. Find the inverse Laplace transform of 1/(s² + 4s + 5) Enter your answer

A: Solution :   Given that  1s2+4s+5