Write a fundamental matrix for the associated homogeneous system

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Q: Find the gen method of un

A: Given,          y''-2y'+y=2x+cosh(x)

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Q: How many solutions are there to the following equation that satisfy the given condition: x₁ + x₂ +…

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Q: A) Evaluate the following integral dx - (x - 1)(x − 2)(x − 3) 10 points

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Q: 8. A spring has a natural length of 10 cm. It takes 2J to stretch the spring to 15 cm. How much work…

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Q: Determine the ordinate of the centroid of the area bounded by the curve x^2 =8y and the line 2x-y=0

A: Given curves are x2=8y and 2x−y=0. We have to find the ordinate of the centroid of the area bounded…

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Q: Q3// Use Newton-Raphson Method to solve f = -x²+x+0.75 for 5 iteration (choose 4-decimal places).…

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Q: SOLVE THE VOLUTION OF THE #F ㄜㄊ y" ty= g(t) = {1, 0≤ t <317 0₁ 773 1 J 9 (₁) = 0 9' (0) = 1

A: Laplace transform of the differential equation

Q: 8. A spring has a natural length of 10 cm. It takes 2J to stretch the spring to 15 cm. How much work…

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Q: (a) A resistance R in series with inductance L is connected with e.m.f E(t) = t. The current i(t) di…

A: Sol

Q: Q3// Use Newton-Raphson Method to solve f = -x²+x+0.75 for 5 iteration (choose 4-decimal places)…

A: This is the question from Numerical Analysis.

Q: Evaluate the Inverse Laplace transformation of the following functions

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Q: 3. Let f: R² → R. Suppose ƒ € C" with ƒ(1, 1) = 1 ; fi(1, 1) = a; f2(1, 1) = b. Let o(x) = f(x,…

A: Given that              f : ℝ2→ℝ  such that  f∈C' with f(1,1)=1;  f1(1,1)=a;  f2(1,1)=b.

Q: Find product solutions of 2 H J² Jx² 4 Ju day

A: Given PDE is ∂2u∂x2=4∂u∂y       (1) Let the product solution be u(x,y)=XY                (2) Putting…

Q: 7. Find the number of different permutations of the letters in the word GIRAFFE.

A: Given: find the number of different permutations of the latters in the word GIRAFFE

Q: The integrating factor of 3xdy + 3y dx is

A: given differential equation: 3xdy+3ydx=0 Remember :  A differential equation of the form…

Q: Find pro J² Jx² duct solutions of 4 du dy

A: The details solution is given below

Q: Let A = {1,2,3}, X = {1,3}, and R is a relation on A, such that R= {(x,y) | X<Y ^ x, y = A} R"X =…

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: Problem 3. For the function f(x) = 6x²-x-2, evaluate and fully simplify each of the following: a)…

A: The solution is given as

Q: (f) The gradient vector Vf at a point x = (₁, 22, 23, ₁) R¹ is given by af af af af V/=( 1 Or Or₂…

A: (i) Gradient of a scalar function f in R3 is given by…

Q: (b) Find the Fourier integral of the function f(x)=e** when x>0 and f(-x) = -f(x) for k>0 sin and…

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Q: solve the following differential equations: a) (2x²³x+ sin (1/2-½x) + y ) dx + (x²y-x) dy = 0 b) (3…

A: Thank you for the question. According to our guidelines we can answer only  first question and…

Q: s) Solve the Boundary Value Problem v²u=0, 0<x<3, 0<y<3 u(0, y) = u(3, y) = 0, 0<y<3 u(x,0) = 0,…

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Q: Q4 Find the area of the region that lies outside the circle r-1 and inside the cardiod r-1-cos ()

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Q: Q3 Find the area that enclosed by the circle r-2sin for T/4 ≤ ≤π/2 (3) V=2sin Bout ()

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Q: Jason thinks he can save enough to deposit P1,200 in the bank at the end of each year for the next…

A: The future value of an annuity is given by FV=PMT×1+in-1iWhereFV=future value of annuityPMT=cash…

Q: How much must a person put into the bank today if he wants $50,000 in 5 years at 6% compounded…

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Q: The result of dy/dx for the following function is COS X y = 1+sin x

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Q: The linear, homogeneous, constant coefficient differential equation of least order that has -4z…

A: we have to find the linear, homogeneous, constant coefficient differential equation of least order…

Q: The inverse of 17 modulo 23 (a) 19 (b) 18 (c) 20 (d) 21

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Q: Consider the following linear transformation and basis. T: R² R2, T(x, y) = (5x - 2y, x), B' = {(-2,…

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Q: Problem 7. a) Describe the transformation(s) that can be applied to the function g(x) = e* to obtain…

A: Transformation of the function  f(x+c) c units left  f(x-c) c units right f(x)+c c…

Q: Prove that the Intermediate Value Theorem remains true when the inequality sign is flipped, i.e.…

A: We know that According to Intermediate Value Theorem: A function is continuous in interval  I = [a ,…

Q: 1) Write the given second order equation as its equivalent system of first order equations. u"…

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Q: For the purpose of our study n nunning

A: We have to write the purpose of the discrete structures and how they will benefit us.

Q: How can the unit circle help us find the exact values of trig expressions involving special angles?…

A: We have to discuss how can the unit circle help us find the exact values of trig expressions…

Q: Q3// Use Newton-Raphson Method to solve f = -x²+x+0.75 for 5 iteration (choose 4-decimal places).…

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Q: If My - Nz Q, where is a function of x only, then the differential N equation M + Ny = 0 has an…

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Q: (b) Find the bacteria count after 0.5 hour. (Round your answer to the nearest whole number.)…

A: Given: The number of bacteria in refrigerated food is given by, N(T)=10T2-20T+550, 1≤T≤20, where T…

Q: Question 3 Give the form of a particular solution of y"" + 2y" +9y' +18y = 3e-4 + sin(3x) - 3x.…

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Q: Find ß so that {1, x, 1+ 6x²) on (-1,1) is orthogonal.

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Q: For the following problems, use the method of shells to approximate the volumes of some common…

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Q: EXAMPLE 2 Consider again our analysis of a heavy rock blown straight up from the ground by a…

A: according to question, velocity of the rock at any time t during its motion is given by  vt=160-32t…

Q: Find the Jacobian of the transformation. x = 4² + uv, y = 2uv² Need Help? Read It

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Q: Determine if the equation specifies a function with independent variable x. If it does, find the…

A: A function is an equation for which any independent variables yields exactly one output.