Use a Fourier transform to solve the following initial value problem for the free Schrödinger equation, where x E R andt> 0: Ut = iurx, u(x, 0) = e-?.

Q: Suppose solving an equation by Laplace transform results in Y(s) = s2 + 64' Evaluate y(7).

A: We have to solve given problem:

Q: I need to use the Laplace Transform to solve the given initial value problem

A: We will solve the given differential equation using Laplace transform method.

Q: The signal x() exp(-at)u(t) is passed as the input to a system with impulse response…

A: We have given a signal ..with the help of the Fourier transform we find energy ..the procedure is…

Q: Use the Laplace transform to solve the following initial-value problem for a first-order equation.…

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Q: Use Laplace transformation to solve the differential equation: y(0) = 1 and y'(0) = -3 y" + 3y'-10y…

A: Use the following formulae, to obtain the solution.…

Q: find the Fourier transform f(x) = e ¹² cos fx|

A: What is Fourier Transformation: A mathematical transformation known as the Fourier transform…

Q: Derive the Fourier spectrum of a signal that is given by z(t) = forect (2T) exp(−j10t + jt) dt.…

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Q: Derive the Fourier transform for f(t) = te2t for t>0 and 0 for t<0.

A: The Fourier transform of the function f(t) is represented as F(k), it is defined as ∫-∞∞e-iktf(t)dt,…

Q: 19. y" + y = t, 2-t, 0, 0 ≤ t < 1, 1≤t < 2, 2 ≤ t < ∞0; y(0) = 0, y'(0) = 0

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Q: y" + y = e sent,

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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: Use the Fourier transform method to solve du k at ax2-Yu, -o∞ 0 u(x, 0) = f(x).

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Q: y" – y' – 2y = 4t², y(0) =1 y'(0) = 4 I| |

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Q: (3) A signal has Fourier transform as, 1 sinc (2w X(w) sinc + 2. Compute x(t)

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Q: · y"(t)+5y'(t)+4y(t) = 0, y(0) = 1, y'(0) = 0

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

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

Q: y" + 9y = 5t + 2, y(0) = 2 y'(0) = -1 |

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Q: y" + 5y' + 4y = 0, y(0) = 1 y'(0) = 0

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Q: Use the Laplace transform to solve the given initial-value problem. у" + 2y" - у' - 2у %3 sin(3t),…

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Q: 3 y" + 9y = sen2t, 2

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Q: Find the fourier transform of f(t) = e-2(t+4)ʻ sin (nt).

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Q: Find the Fourier Transform of x(t) = e-t² and solve fe-t² dt

A: To Do: Find the Fourier Transform of xt=e-t2. Also, solve ∫-∞∞e-t2dt.

Q: x'(t) = 2 x(t) – 3 y(t) ; y'(t) = y(t) – 2 x(t) doğrusal diferansiyel denklem ninin x(0) = 0 , y(0)…

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Q: Find the fourier trans y (t) = x (+). Cos wot

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