Use the Laplace transform to solve x₁ = 2x1 + 3x₂ + 12e¹ x2 = x1 +4x2 with initial data x₁ (0) = -8 and x2 (0) = 2.

Q: Find inverse Fourier transform of F(W) %3D W2-2W+3

A: A complex domain function can be transformed into a real-time function through the inverse Fourier…

Q: Describe in your own words the method you would use to find the Laplace transform of the first…

A: The Laplace transform of function f(t) is given by Lft=∫0∞e-stft dt and is denoted by F(s). We can…

Q: Compute the Fourier Transform of f(x) = e-ax-

A: Fourier transform of a function fx is defined as  Ffx=∫-∞∞fxeisx dx Gamma function =∫0∞e-x xn-1 dx

Q: g(t) = 10rect [²(t+³)] ej²¹ 5 ej²nfot j2πfot

A: What is Fourier Transformation: A Fourier transform (FT) is a mathematical transformation that…

Q: Find a linear differential operator that annihilates the given function 1+6x-4x3

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Q: L-1{ 1 (s2+1)(s2+4s+8)

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Q: Find the inverse fourier transform of f (p) =e

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Q: Calculate the fourier transform F (P) following function: f(x) = ¹/2x²(x³ + 3x²-5x) OF # Where F(p1…

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Q: Show that A = has two different factorizations of the form A = L · U where L is lower triangular…

A: Given: A=0001. To show: A has two different factorization of the form A=L·U, where L is lower…

Q: I. Perform the indicated multiplication on the differential operator D. (xD -8)(xD +3)

A: Solution :-

Q: t3 - 3t2 + 5t – 8

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Q: Consider the function -1< x < 0 0 <x < 1 f(x) = { 1202 +1 f(x + 2) = f(x) and Find the Fourier…

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Q: Compute the Fourier transform of the following function: f(x) = e-a(r-x0)²+iqx (5) where a > 0 and q…

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Q: nsform of 20 sinc (10(t - 10)

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Q: • Let: X₁ (jw) = 2nd(w) + nd(w − 4ñ) + ñ8(w + 4π) • Use the inverse Fourier Transform to find x₁(t)…

A: Introduction: Like other integral transformation, Fourier transformation has also its inverse. In…

Q: Find the function f(x) that has Fourier transform (k) = (1+k4)-1.

A: Here we have to find out  .Now from definition of inverse fourier transform , to evaluate this…

Q: Find the Exponential Fourier coefficient Cn for signal f(x) = x Defined on interval [-1 ,1]

A: Complex form of Fourier series is defined as follows: fx=∑n=-∞∞cne-inx2πL where,…

Q: Use (8), to evaluate the given inverse transform. (Write your answer as a function of t.) (t) dt =…

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Q: what is the discrete fourier transform of y = 001010

A: Introduction: Discrete Fourier transformation is applied when the signal is discrete and finite. For…

Q: Obtain the Fourier transform of the function where f(x) = 0 for x &lt; 0 and f(x) = e−axsin(bx) for…

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Q: Find the Fourier Transforms of the indicated function: f (x) = xe-|x|

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Q: Use Laplace transform technique to solve y+2y+2y=e, y(0) = 3, y (0)=-3

A: We need to use Laplace transform to solve this differential equation.

Q: Let f(x) = (x2 + 1), n<x <a be a periodic function, then the Fourier coefficient az = Answer:

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Q: The graph f(x)=x^2 was transformred to create k(x)=f(x-5)+1.  Which of the following represents…

A: Plot a table for the values of the x and f(x).xf(x)-24-11001124Draw the graph of x vs f(x).

Q: Find the inverse Transform F (6) = 6s s?+25 3. s²+25 S + 2

A: Note the result :

Q: Find the Fourier Transform of f(s) = e-ax= a >0

A: The Fourier transform of a function  is given by :

Q: * - 10x + 9x = 5t, x(0) = -1, x(0) = 2

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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…

Q: fer) sen ax %3D

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Q: Solve the fourier transform of the following functions: 2. f(x) = {x if 0 < x < a otherwise

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Q: 5. Find the general solution to x₁ = 4x₁ + 2x₂ + 3et, x₂ = 2x₁ + x₂ + et using Laplace transform.

A: The given system of differential equation is  x1'=4x1+2x2+3etx2'=2x1+x2+et To find the general…