9(x) = ² + (x-1)e-x)(1) dt. 0

Q: f (t) ) — е -4(t-2)² e

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Q: y" + y = √2 sen √2t, y(0) = 10, y'(0) = 0

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Q: 1 | (1 – 4æ)7 dæ

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Q: olution, find 1 - Using convo a. L-1 s² + s-6

A: If the Laplace transform of functions f(t) and g(t) are F(s) and G(s) respectively, then and…

Q: -jwt dt ーの 2. 70

A: We have to solve given problem:

Q: (cos(t - 27/3 ) t> 2/3 .Find I f(t) if f(t) = t<0

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Q: 2 Calculate the inverse Laplace of by using Convolution theorem s(s2 +2s+4)

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Q: Determine L-1. 2s² +10s (2s²-20s+58) (s+1)

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Q: Find the Laplace Transform of the function. Show your work. f(x) = sinh(ax)

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Q: 10. Find the Laplace transform of 10 cos Tt (1 < t < 2)

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Q: 2 The inverse Laplace transform by using integral of transform s(s2 +2s+4)

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Q: a) 2-3u(t-5) cost = -t Find the 33 Ordine Lap of

A: The given function is ht=-t cos5t-3ut-5cost To find: the Laplace transform of the given function.

Q: 3s – 137 L(f) s2 + 2s + 401

A:

Q: lle s [ (s+5) ³ ] Use convolution to find L-19

A: Let's find inverse laplace by using convolution theorem.

Q: 10. Solve F (1) =1 +2 F (t- u) e 2" du.

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Q: (~6 }] រឺ ទ 1 sh 2 2. x< 2x

A: Given function is gx-π=0x&lt;π12sin 2xx≥π. To find: Solution of the function using Laplace unit step…

Q: Find the Laplace transform of f(t)=u(t− 3)(2t² +1)+2e³ cos²t

A: The objective is to find the laplace transform of f(t).

Q: e. L-1 1 S3 +9s

A: Note: According to the guidelines we are allowed to solve one question at a time. So please post…

Q: Problem 1: Solve the following Initial Value Problem: y" – 4y' + 5y = 4e", y(0) = 2, y' (0) = 7 %3D…

A: Answer is mentioned below

Q: L[e-3tcos (3t) + 3e-3tsin (3t)]

A: The solution is given as

Q: Use the Laplace transform to solve 1 x = 4x + 1y y' = x(t) = y(t) = - 29x - 6y x(0) = 2, y(0) = - 12

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Q: -15 10] 4 -1 8. 10 2.

A: Solution is given below:

Q: Find F(s) for f(t) = sin? 4t

A: Solution

Q: x"(t) + 4x" (t) + 9x'(t) + 10x(t) = -24te'; when t = 0, x = 0, x' = -4, x" = 10

A: Use Laplace table

Q: a) Given that f(t) = {(tt) ((t-1)² e3t 0 ≤t≤1 t>1 i) Find Laplace of f(t) using the definition of…

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Q: (5) Based on part (4), the solution of the problem (E) is: a. u(x, t) = v(x, t) + e" – x + 1. b.…

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