Solve the differential equation: y' = 2et; y(0) = -1 A. y = 2et – 1 C. y = 2et – 3 B. y = 2et – 2 D. y = 2et – 4

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A: We are given : -3(1-cosh 377t)t Let, f(t)=-3(1-cosh 377t)t Now, L-3(1-cosh…

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Q: Determine the Laplace Transform of the following functions. Show your detailed solutions. sunt-1 5.…

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Q: Find the Inverse Laplace transform of the following: (3s+2) / (s2+25) (5s2+3) / (s2+4)2

A: Part (i): Given,

Q: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

A: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

Q: Q1/ Find the laplace transform for the following 1 - e-6t.sin(10t-8)

A: By using properties of Laplace transform we solve the given problem as follows :

Q: Calculate the Inverse Laplace transform of the following. Please write down all the steps of your…

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A: We have to write f(t) using step function and find the laplace transform. Also, draw the graph.

Q: L{e-2t cos3t}

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Q: Determine the Laplace transform of the following function f(x) = x2 1. f(x) = e®, a E R 2.

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Q: sinh ot + cos ot

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Q: What would be the laplace transform of a function of f or L{f(t)}?

A: Given: What would be the Laplace transform of a function of f or L{f(t)}?

Q: Find the Laplace transform of f(t) = sin² 5t a. 50/($³+125s) 25/(s³+ 100s) b. C. 25/(s³ + 125s) d.…

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Q: Find the inverse Laplace transform of [(18s)/((s2+9)2)]e-2s

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Q: F(s) = 8 $³-3s²-4s 00

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Q: e^3(t+2)/2. Find laplace transform of the function

A: Let's find Laplace transform of given function.

Q: Find Laplace transform for the function f(t) = 3 sin 4t .

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Q: What is the Laplace transform of (1 + e4t)?

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Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

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Q: 2. Determine the Laplace transform of the given function using the Table coshbt te3t sin2 t

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Q: Find the la place transform of the following. Simplify your answer f(+) = sin3t Sinht

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Q: Use formulas from this course to find the inverse Laplace transform (a) L-1{+1) 2s+1 1 252+8 (b)…

A: Solution:

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Q: (b) f (x) = {sent, .if 0<t<n l0, if

A: We find Laplace transform of given function

Q: i{tsinst t}

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Q: Q2/ Find Fourier Transform the following function as in graph: (-1,0) (1,0) Pi

A: The given problem is to find the Fourier transform of the given function in the graph. We have to…

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A: We have to find Laplace transform of given function using Definition.

Q: y(t) =1– |(7)e*dt

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