Consider the nonhomogeneous differential equation: -2y+ y = - (E). Given that 3=e" and y₁=xe are two linearly independent solutions of (E). Using variation of parameters, we find that: U₁ = -√x√x and U₂ = 2√x This Option None of these u₁ = x and u₂ == This Option u₁ = -lnx and u₂ = This Option J|X

Q: 6. Consider the set Zn under the operation of multiplication. (a) Build a Cayley table for n = 5 and…

A: We now construct the cayley table fot (Z5,.) And (Z6,.)

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A: The region D is enclosed by  y=7x,x=7,y=7xto find the value of  ∫∫D14ydA

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Q: 3. (Complex Numbers: Quadratic Equations; Scientific Calculators). Solve the quadratic equation 2² +…

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Q: Express the set using the roster method. the set of natural numbers less than or equal to 6.

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Q: Find the exact sum of the following series 3 0 In (²) 2 3 5 010 ( 17 ) - 1/1/2 ln 2 3 2 (²) - ²/3 2…

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Q: ! Consider the nonhomogeneous differential equation: y" - 2y + y ==... (E). Using variation of…

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Q: 1. Evaluate the following integral S² a. Analytically b. Numerically using: -20 20x7 + 5x5 + 15x³ +…

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Q: ! %A1. The solution of the exact differential equation (2xy² - 3)dx + (2x²y + 4)dy = 0 is: x²y²-3x =…

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Q: Question 2. Solve the homogeneous system of linear equations 3x¹ - x² + x³ = 0 -x¹ +7x² - 2x³ = 0…

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Q: 13. In finding a smooth piecewise parametrization of path C, A. the direction of the sub-paths must…

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Q: (a) To determine To compute: The initial value problem + 4x = sin 4t with initial conditions x (0) =…

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Q: a. 1, 1, 2, 3, 5, 8, 13, b. -2,3, 4, 5, -6, 7,

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Q: Find the centroid of the region bounded by y=x+3 and y=x²-3. O (1.098,1.68) O (0,1.68) O (1.68,…

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Q: f(t) = 5te-²t cos(3t)

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Q: 3. Determine the Fourier transform of the following: f(t) = {el³6 0, -1 < t < 1 elsewhere

A: Fourier transform of f(t) F(f(t))=∫-∞∞f(t).ejstdt given function f(t)=ej3t-1&lt;t&lt;10elsewhere

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Q: Which of the following is an "even" function of t? Ot² t²-4t sin(2t) + 3t O +³ +6

A: Even Function - For a real-valued function f(t), when the output value of f(-t) is the same as f(t),…

Q: Fill in the blanks by using either E, E, C or £. -) Q---R ) -0.60 =) π --Z

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Q: 9. (a) Express 2 2¹-1² as partial fractions. (b) Hence, compute the exact value of the following…

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Q: If ƒ` = (x+1)√/x² + y i + ² tan^¹(3x−y)j and ğ=- y at (0,1,²7) 4 find: fxcurl ğ +(g.V)ƒ at x + y…

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Q: Find the general solution of the differential equation y" + 4y = 13 sec² (2t), 0 < t < </ 4 NOTE:…

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Q: - Solve the initial value problem 25y" − 40y' + 16y = 0, y(0) = 2, y'(0) = 3. Choose one Decreasing…

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Q: Find the solution of the given initial value problem. 5y""+120y' 800y = 0; y(0) = 11, y'(0) = 26,…

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Q: 1. Evaluate the following integral ľ a. Analytically b. Numerically using: 20 20x7 + 5x5 + 15x³ +…

A: Note:- As per our guidelines, we can answer the first three sub-parts of any problem. For the…