10. Solve the following IVP using Fourier Transform: -00 < x < oo, t> 0, u(x,0) = e, -0

Q: 1. f(t) = 5(e^-4t)[cos(10t)] A. (5s – 20) / (s^2 - 8s + 116) B. (s - 4) / (s^2 - 8s + 116) C. 50 /…

A: Laplace transferom of the function

Q: (28x if |x|1* Find the Fourier transform of (x) = { %3D

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Q: Laplace transform of {(e^2-t)U(t-2)}

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Q: Solve using Laplace transform y"-2y' +5y=1+t, y(0)=0, y'(0)=4

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Q: 4. f(t) = e^(5t)(t^3) A. 6/ (s-5)^4 B. 6/ (s+5)^4 C. 6/ (s-5)^3 D. 6/ (s+5)^3 %3D

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Q: Laplace Transform. Please show your complete solution

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Q: Use Laplace transform technique to solve y +2y +2y= e-, y(0) = - 4, y'(0) = - 2

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Q: What the similarities and differences between Laplace transform and the undetermined coefficients…

A: To give similarities and differences between the Laplace transform method and the method of…

Q: 8.(a) Find the Fourier transform for the function cos x, -n/2 7/2 f(x) = 0, (b) Use the result in…

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Q: Use Laplace transform technique to solve , y"-y'-6y= 0, Given y(0) = 1 and y'(0) = -1

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Q: Use the laplace transform to solve 3x'-y=2r;x'+y'-y=0; x(0)=y(0)=0

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Q: Find the Fourier Cosine Transform of the function 031.png ... f(x)= (ae¯mx + hex} if x>0 -nx if a =…

A: Please check step 2 and 3 for the solution.

Q: 2e 5(s+1) (a) Determine I |(s+4)' ` s² +2s +5 3.

A: As per the company's guidelines, we are supposed to solve the first question for you, kindly repost…

Q: 3. f(t) = [sin(2t)]^2 %3D

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Q: 235 óf the textbc (d) F{e* ,5iz-az²

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Q: Find the inverse laplace transform of the followings; a)  X(s)=(s+2)/(s^2+2s+5)…

A: a) Xs=s+2s2+2s+5 Apply Laplace Inverse transform…

Q: Use Laplace transform to solve the following IVP y′′(t) = 4y(t) −e^(−t)U(t −1), y(0) = y′(0) = 0.

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Q: y"+2"-z' = 0 y' + z 221-ex - Yo = 0, y = 1 20= 1, 2 = 1

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Q: Use the laplace transform to solve 3r'-y=21;x'+y'-y=0; x(0)=y(0)=0

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Q: 5) Use Laplace transform to solve the integrol epuation it f(t) = cost + (*- tau) e

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Q: f(x)= == ¹xcl! Obtain the Fourier transform of

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Q: Sº 2 19. s³ +85² + 7s

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Q: 1. Deduce the continuous function whose Laplace Transform is 10 F(p) P (p² + 9) 2.Find Р2—ЗР+10 (i)…

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Q: Use the InverseFourierTransform function of Mathematica or Wolfram Alpha to find the (spatial)…

A: We are given the spatial Fourier transform of a spatio-temporal function u(x,t) as : u(k,t) =…

Q: What is the Fourier transform of 8(x) dx F(k) = 100 = 2T -ikx 8(x) =?

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Use (8), • S* f(1) dt = £^¹{F(5)}, to evaluate the given inverse transform. (Write your answer as a…

A: we know that laplace transform of e^(at) is (1/(s-a)).

Q: Suppose solving an equation by Laplace transform results in 4 (s+ 18) Y (s) : %3D (s+9)² * Evaluate…

A: Laplace transform of the function y(t) is defined as Y(s)=∫0∞e-sty(t)dt, where s&gt;0. Since the…

Q: Find the Laplace transform of (e^ (2t)) sinh (4t) (-s^3 + 11s 2 1. (e^ (3t)) cos (5t). A. 56s + 196)…

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Q: Give the Inverse Laplace Transform of s/((s+2)(s^2+4)). * O -1 + (e^(2t))cos(3t) O t+ (9/4)e^(-2t) -…

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Q: Suppose the Fourier transform F(w)=re-lwl, is known. Show that the inverse Fourier transform, viz.,…

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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…