By using the Fourier transform, find a solution for the following problem (PJu,(1, x) = ux(!, x) + 3f², xe R, 1 > 0 u(0, x) = sin(x), xER

Q: 31²+1 dt = Compute:

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: Prove that •1 to(xt) 1-1² dt = Sinx x

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Q: Use the Laplace transform to solve the difference equation 3x(t) — 4x(t − 1) = 1, x(t)=0 for t < 0.

A: Given: The difference equation, 3xt-4xt-1=1, xt=0 for t&lt;0   To solve: The given difference…

Q: [(x²-y²)²] x+y -2 LEK 1J0 du dt

A: We have to find value of given double Integral.

Q: (d) Use Fourier Sine transform to solve: a'u du əx² ay² 00; [u(0,y)=0, u(x,0)=f(x); (u(x,y) →0, as…

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Q: f(t) = {, - 2 2 -2

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Q: Use Laplace transforms to solve the IVP y''-y=0, y(0)=2, y'(0)=3. Show the complete solution.

A: Given initial value problem is, y''-y=0, y(0)=2, y'(0)=3

Q: For the linear operator L = D^2 −4D + 8, determine L(y) for y = e^(2t), y = e^(2t)sin(2t), and y =…

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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: Find the Fourier sine expansion of f(x)=x² (3L– 2x) on [0, L].

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: use LaPlace transforms find solutions for dx/dt+3x=e^-2t, given that t=0 and x=2.

A: The objective of this question is to solve the given differential equation dx/dt + 3x = e^-2t using…

Q: 1. Let F : L² (R¹) → L²(R¹) be the Fourier transform. That is: 1 F(f) = = √e-i(+1) e-i(x,x) f(x) dx.…

A: Problem is solved using concept of Fourier Transform.

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

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Q: x^2y′′ + (3/2xy′ + [(1/36)x^2/3 − 7/144]y = 0 z = (1/2)x^1/3, w = yx^1/4 Solve it using the…

A: The transform method can be used to find the solution to the differential equation x^2y′′ + (3/2xy′…

Q: By using a suitable Fourier transform, the solution of 9u

A: In this question, we have to solve the wave equation by using Fourier transform. The wave equation…

Q: Compute N(0) if r(t)= and prove that T(0) and N(0) are orthogonal

A: Given rt=&lt;t sin t+cos t,2t2,sin t -t cos y&gt; Then vector is given by r→t=t sin t+cos…

Q: (a) y'=ty (3-y), (b) y'=y (3-ty), (c) y'= -y (3-ty), (d) y'=t-1-y², y(0) = yo y(0) = yo y(0) = yo…

A: We will be graphing the slope field of the given differential equation along with the interpretation…

Q: Let f(x)=2 cos(5x)+3 sin(4x) and let q, be the Fourier polynomial of degree n for f. (a) Show that…

A: Given: fx=2cos5x+3sin4x The period is 2π as f2π+x=fx The fourier polynomial of degree n is:…

Q: Determine coefficients a and b such that p(x)=x^2+ax+b satisfies p(1)=6 and p′(1)=0

A: Since you have posted multiple question in this question which are nt interlinked so i have solved…

Q: 2) find the fourier transform x(t) = u(t) x(t) ulzt) x²(t) = u(+ + 5) -

A: xt=utxt=u2txt=ut+5xt=ute-jw0t

Q: -2sin4t Determine the Laplace transform of the equation f (x) = 2 e´ 10 A s²+4s+20 8 B s²+4s+ 20 20…

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Q: Q3) Verify that the Fourier transform of the function [1–|x|, 1-|x|, |x|1 ƒ (x) = = { 1 + 0 is ƒ…

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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: find the derivatives complex funcation. {tanh¬'(iz +2)}-1,

A: fz=tanh-1iz+2-1=1tanh-1iz+2 It is known that tanh-1x=11-x2 so it follows:…

Q: Solve the IVP x”+9x = U(t-2)sin[3(t-2)], x(0)=2, x’(0)=0 using Laplace Transforms. Identify xc , xp…

A: The solution is given as

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: Let F = (t + 4) i +² sin(41) j+ t^k, G = e' i+ 4f* cos(t) j+ e$t* k and 512 -i+ 4² j+te²ª k 1 +t H =…

A: Given :  F=(t+4)i+t^ 2 sin(4t)j+t^ 4 k G=e^ t i+4t^ 4 cos(t)j+e^ 5t^ 2  H = (t ^ 5)/(1 + t) * i + 4t…

Q: Prove that the Fourier transforım of f' (x), the derivative of f (x) is – ip f (p), where S(p) is…

A: Answer: For the given data,

Q: 0.x 1

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Q: kx _f(x) = ek

A: The Fourier integral of a function f(x) is defined as:F(ω)=∫−∞∞f(x)e−iωxdxTo find the Fourier…

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

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Q: use LaPlace transforms find solutions for dx/dt+3x=e^-2t, given that t=0 and x=5.

A: The objective of this question is to solve the given differential equation dx/dt + 3x = e^-2t using…

Q: Calculate the Fourier transforms of the following functions (you do not need to use any complex…

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