The function y₁ = x². ln(x) is a solution to the DE, x²y"-3xy' +4y=0. Use the reduction of order formula to find a second linearly independent solution. Show all work for any integrals. 2.

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Q: list the days during the next 60 days on which megan and michele will see each other in city b

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Q: 8. d²y dy Solve the Cauchy-Euler equation x²- +8x +6y=0. dx² dx

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Q: 12. Determine whether each of these functions from Z to Z is one-to-one. If not one-to-one, give…

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Q: 1. Find all solutions of the congruence 5x+3x²+x+3 = 0 mod 30.

A: The congruence .To Find:Solution of the above congruence.

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A: Consider the matrix A given below.A = [[0, - 1, 0], [- 6, 1, 0], [6, 2, 3]]Determine if x = [[5],…

Q: 1b) y" + 20y + 100y=p+qe, y (0) = 0, y (0)=0 where p= 100h, q=20h (av - 5), r = av Decompose the…

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Q: 15. 10 Σ 2+1 – 2 i=0 What is the value the sums of terms of a geometric progression

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Q: B. Express the ff atticher whit with general Form quadortic function. 1. 2 9=C++3) ²-3 FLAMU

A: The general form of a quadratic function is

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A: We find Nth partial sum of this series

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Q: 3. Solve the system of congruences Show the steps used. 3x = 2 7x 3 8x7 mod 7 mod 11 mod 19.

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Q: Prove that 1^2 - 2^2 + 3^2 +...+(-1)^(n+1)n^2 = (-1)^(n+1)n(n+1)/2 for all n∊N.

A: We will prove the given result by principle of mathematical induction.

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Q: 1. Consider the following function, sin 1(2) - (2²46² (²) ƒ(x): if x = 0 if x = 0 Prove that the…

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Q: part (b), why is it equal to 0?

A: We have find  why part b is equal to 0

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Q: (c) Prove that the set of congruence classes modulo m is a commutative ring.

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Q: 3. Complete the square and state the vertex, for the following equation=-0.1x² – 0.6x – 0.4.

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Q: Which statement isnt and can never be true? MA Sinx = COS X B COSX = 0944 sinx + cosx = tan x So 0 -…

A: We choose a statement which can never be true.

Q: 2. Write a proper L.S. R.S. proof for each of the following trigonometric relations. a. cos²x+cot² x…

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Q: Let F be a field and let n be a positive integer. Then There exists a primitive nth root of unity in…

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Q: Determine the number of permutations (arrangements) possible of 7 things taken 3 at a time.

A: We have to determine the number of possible permutations of 7 things taken  at a time.So,

Q: 11. a) U₁₁ A₁ Let A₁ = {i,i+1,i+2,...} for i=1,2,3,.... Find b) Ai

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Q: Tim's gross pay is $1568. The amount of Social security deducted is 6.2% of gross pay. How much of…

A: Given that Tim's gross pay is $1568 and the amount of Social Security deducted is 6.2% of gross pay.

Q: Prove that for every integer n ≥ 3, (1¹ – 31) (¹ − 4 ) ··· (1¹ – ²/1 ) - 32 (n+1)(n+2) 6n(n − 1)

A: Let the given statement is          we will prove the above statement by using mathematical…