Show that the change of variables y = x/2u trans- forms the differential equation y"+(1-) -0 3 y 0 4x2 into the Bessel equation x?u" + xu' + (x2 - 1)u = 0 and thereby write the general solution to the given dif- ferential equation.

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Q: Let α be a zero of x3 + x2 + 1 in some extension field of Z2. Solve the equation (α + 1) x + α = α2…

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Q: Let α be a zero of f (x) = x2 + 2x + 2 in some extension field of Z3.Find the other zero of f (x) in…

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A: Let d be an integer less that 1 that is not divisible by square of a prime. To prove that only units…

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Q: This question concerns the following two subsets of R4.noitulos won ni S = {(0,1,3,2), (1,0, 1,0),…

A: Given : Two subsets of ℝ4 : S = {(0, 1, 3, 2), (1, 0, 1, 0), (1, -1, -1, -1)} ,T = {(a, b, a+b+c, c)…

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Q: Which of the following is the general solution of the difeerential equation d'y dy -2 + 5y=0? dx2 dx…

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Q: ii. Prove that if n+1 E R", then {₁,..., n, n+1} are not linearly independent. (b) Suppose that x,…

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Q: 2. If f(x, y, z) x³y²z4 find the stationary point of f(x, y, z) on the plane 3x - 2y and the value…

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Q: 7) f(x)= xe-x 0 if -1<x<0 otherwise

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Q: Compute y = F 8c by the three FFT steps for c = (1, 0, 1, 0, 1, 0, 1, 0). Repeat the computation for…

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Q: Prove the function is convex function T f(x, y) = log (ex+ey) where x, y € RT E

A: fx,y=logex+ey

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Q: f(x) = 0 if -1<x otherwi

A: Formula for the Fourier Transform of fx is  Fw=∫-∞∞fxeiwxdx We are given fx=|x|if…

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Q: 1. Let B = (B₁)tzo be a standard Brownian motion started at zero, and let (FB)zo denote the natural…

A: note : Since you have posted multiple questions with multiple sub parts, we will provide the…

Q: 3 2 25 +5² +85 +6 (S²+4) (S²+1)

A: Given that L-12s3+s2+8s+6s2+4s2+1

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Q: 3. Let A be a n x n matrix with distinct and positive eigenvalues. For each i, 1 ≤ i ≤n, let v, be…

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Q: Given a compact set A and a closed set B. ShOw that AB is compact!

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Q: Find the value of the constant  C for which the integral integral 0 to infinity [ (x /  x2 +1    ) -…

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Q: If A is a Markov matrix, why doesn't I+ A+ A2 + · · · add up to (I -A)-1?

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Q: it needs matlab code  these functions in MATLAB code

A: Required Matlab code: syms x syms b lim((sin(bx))/x, b, inf)

Q: Show that if m₁,..., mn are integers, then the number mj - mi j-i II 1<i<j≤n is an integer. (Hint:…

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Q: Let b be a zero of f(x) = x5 + 2x + 4 Show that none of √2, ∛2, ∜2 belongs to Q(β).

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Q: How are the eigenvalues of AH related to the eigenvalues of the square matrix A?

A: Given: The eigenvalues of AH and the eigenvalues of the square matrix A.To find: The relation…

Q: 4 Let x € [0, 1]. Show that ge 2 satisfying f(x)= 5 FC f(t) gx (t) dt & feu

A: