4. 4w + 2x + Зу %3D 5 2w + 3x + z = 2 3w + 5x + 2z = 3 4х + Зу + 6z%3D 1

Q: 1² +2²+ •+n² = n(n+1)(2n+1) 6 for n EN

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Q: F(s) = 1 (s²+4) (s²+4s+8)

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Q: Consider the following IVP: y"-3y'+2y = e*; y(0) = 0, y'(0) = 0 Find the general solution.

A: We solve the given DE  y"-3y'+2y=e3t.......(1) y(0)=y'(0)=0......(2)

Q: 5*) y" + 4y = u₁ (t) — u₂ (t), y(0) = 0, y'(0) = 1

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Q: Зх — Зу — 6z %3D —3 2х — 2у — 4z %3D 10 2х + Зу + z %3D7 -

A: Given system of equations, 3 x-3 y-6 z=-32 x-2 y-4 z=102 x+3 y+z=7 The objective is to solve the…

Q: Let A = -127 0 -8 4 0 and 6- = 36 7 Define the linear transformation T: R2 → R³ by T(x) = Ar. Find a…

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Q: y" + 4y' + 3y = U (t – n)e-2(t-r), y(0) = 0, y'(0) = 0. %3D

A: Consider the provided question,

Q: ST,¥. xキマ 1. Verify C ノyジ * =ンycO

A: Since, we are asked to solve using Stokes theorem only, we will use theorem to evaluate the integral…

Q: Part A Prove the following theorem using either regular or strong induction. Theorem: Suppose that n…

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Q: Prove this theorem.

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Q: Part B Here are three attempted inductive proofs of the correct theorem. None of them are correct.…

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Could you derive the equation from this for βi that is used by the Newton algorithm

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Q: 2. y" — у %3D 4 cost у (0) — 0 y'(0) = 1

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Q: Consider the following IVP: y" -3y' -10y = 1, y(0) = -1, y'(0) = 2 Find the general solution. 13 5r…

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Q: dy 2х dx - y = 6e3t, dt dt dy 3x + dt dx - 3y = 6e3t; | dt x(0) = 3, У (0) 3 0.

A: Given, dxdt-2x-dydt-y=6e3t2dxdt-3x+dydt-3y=6e3t, x0=0, y0=0   We use the Laplace transforms…

Q: Find the Laplace transform Long method

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Q: Solve the equation subject to the given conditions. d'y dy dx² dx 6y=4, y(0)=3, y'(0)=2

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Q: (х — 4у— 7z — w %3D y + z – 2w = -3 х + 2у — z %3D 2 (2х + 4у +z — Зw %3D — 2 –19 %3D

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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: Consider the following IVP: y"- y = 4cos t; y(0) = 0, y'(0) = 1 Find the general solution. A y (1) =…

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Q: Solve for the Laplace transform cosh2t

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Q: a'(t) = -x(t – 1), x(t) = 1 on [-1,0], is given by 1(t) = E(-1)* t – (k – 1))* k! for n-1<t <n, k=0

A: As per the question we are given the following first order time varient differential equation :…

Q: Numerical Maximization: Suppose we want to maximize this likelihood with respect to 3: TI 1 L(B|y₁,…

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Q: (P^Q)^(P = ¬(Q^R))^(S = R) = -S

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Q: Solve Laplace Transform. Show all work, please.

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Q: Q18: y′ − 2y + [y(2) dz=e², y(0) = 0.

A: The given equation is         y' - 2y + ∫0tyzdz = et  . . . . . . (1)     With condition y(0) = 0 .…

Q: " + 8y' + 25y = 13e-2t y(0) = -1, y' (0) = 18 %3D

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Q: 5. L-1(++: = e-2x + cos 2x +sin v3x V3 = e s+2 s2+4 s2+3/

A: From the given problem: L-11s+2+ss2+4+1s2+3=e-2x+cos2x+13sin3x As we know that:…

Q: Prove this theorem.

A: First Isomorphism theorem for Rings: Let ϕ be a ring homomorphism from R to S. Then the mapping…