Question 5. Solve for y(x) given that y"+12y +37y--222 subject to y(0) = -9 and y'(0) = 22. (1) write down and solve the associated auxiliary equation (ii) hence determine the natural response function (complementary function). (iii) determine the forced response function (particular integral) (iv) hence find an expression for y(a) which satisfies both the differential equation and the given initial conditions. Note that although the question is in four parts, this is for your guidance only. For this question please just enter the form of the particular solution, as a function of a in the following box:

Q: Define T: R3→R3 by T(v) = projuv, where u = (0, 1, 2).(a) Find A, the standard matrix for T.(b) Let…

A: As per the question we are given a linear transformation T : ℝ3 → ℝ3 as T(v) = proju(v) , where u =…

Q: ect-) = Σ Στ n=-0 Jn(x) tn 1. Jn(u + v) = ∞ Σ1 Σ Js(u) Jn-s(v) S=-0

A:

Q: 4. Determine the convergence of 3n (n²) n! a. b. Σ 3 Σ- 2 r(Inr)² r=2 T

A:

Q: A linear transformation Tis determined when we know T(i), T(j), T(k). For an affine transformation…

A: As per the question we are given the following statement : "A linear transformation T is determined…

Q: Approximate the arc length of the graph of the function f(x) = x3 over the interval [0, 4] in three…

A: Given:The graph of the function fx=x3 over the interval 0, 4. We have to find the arc length of the…

Q: 2. Using the following data to find the Lagrange polynomials P4(x), P(x), P4 (0.5) and P(0.5). 0.0…

A: 2. Given that the following data xi 0.0 1.0 3.0 5.0 9.0 yi 2.0 0.0 -1.0 3.0 5.0

Q: Exercise. Suppose that (X, p) is a metric space. a) Prove that the intersection of any collection of…

A:

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)…

Q: 1. Let A be a real n x n symmetric matrix, (a) Prove that if A is positive definite, A is…

A: a) Given A is real symmetric positive definite matrix  Which implies all eigen values of A are non…

Q: Find the vector in Span{(1,1,1,1), (1,0,2,-1)} that is closest to (1,0,0,0).

A:

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

A:

Q: if f(z)=u(x,y)+iv(x,y)=z^2+3z+4 find u & v

A:

Q: 1. Suppose u = : (1, 2, 3), v = (2, -3, -4), and w = (1, 0, -2). (a) Find u 2v + 3w. (b) Write the…

A:

Q: Evaluate the integral ∬R(x2+y2)dxdy, where R is bounded by the lines y=x, y=x+a, y=a, y=2a (a>0).

A: The region is bounded by  y=xy=x+ay=ay=2a We have to evaluate ∬R x2+y2 dx dy.

Q: The following problem is about Fundamental Theorem Integral Calculus (-4,1) (-2,3) (-1,0) 3 2 1…

A: From the symmetry of given figure we assume that the parabolic curve passes y axis at y=-1.

Q: Write down the 4 by 4 matrix S that scales by a constant c. Multiply ST and also TS, where T is…

A: As per the question we are given the following 4×4 transformation matrices : S : scaling matrix of…

Q: 3. Suppose f: Rk R, and f = B(R)/B(R). Let X₁,..., X be random variables on (S2, B). Then f(Xí, ...…

A: Given : f : ℝk ↦ ℝ, and f ∈ B(ℝk)/B(ℝ). X1,..., Xk be random variables on (Ω, B) .   To show :…

Q: Question 5. Solve for y(z) given that y"+12y +37y--222 subject to y(0) = -9 and y'(0) - 22. (1)…

A:

Q: A diamond (see the figure below) is a quadrilateral with four sides of equal length. Its diagonals…

A: As per the question we are given a diamond shape which is a quadrilateral with four sides of equal…

Q: [an] 2. If A is similar to a diagonal matrix D then A is similar to AT.

A:

Q: solve d2y 2 - 3 - ㅊ +2y = 즈가

A: This is linear equation with constant coefficients.Let's compose the characteristic…

Q: What are the eigenvectors of the following matrix:  [1 1] [4 1]

A:

Q: Find the slope and the y-intercept of the graph of the linear equation. Then write the equation of…

A:

Q: Exercise. Suppose that (X, p) is a metric space. a) Prove that any set in X consisting of precisely…

A:

Q: 0 1 2 -1 . o 20 3

A:

Q: SetA = round(10 ∗ rand(10, 5)) and s = svd(A) Set[U, D, V ] = svd(A);D(5, 5) = 0;B = U ∗ D ∗ V' The…

A: In this analysis, we are given a matrix A and its singular value decomposition (SVD). We create new…

Q: Find the principal argument Argz when - 2 (a) z = (b) z = (√3-i)⁰. 1+√√3i Ans. (a) 2л/3; (b) . ; 6

A:

Q: Let A, B, and C be sets in a universal set U. We are given n(U) = 88, n(A) = 47, n(B) = 42, n(C) =…

A: Given : n(U) = 88, n(A) = 47, n(B) = 42, n(C) = 50, n(A ∩ B) = 26, n(A ∩ C) = 23, n(B ∩ C) = 23, n(A…

Q: ACTIVITY: Solve the given logarithmic equation. log3 (7x + 3) = log3 (5x + 9)

A:

Q: = (-1/2 =²) A = (c) Use your answer to (a) to find a basis for R2 consisting of eigenvectors of T.…

A: Find the solution of the (c) part.

Q: determine two linearly independent solutions to the given differential equation on (0,∞). Q.…

A: Solutions of a differential equation are functions which satisfies the differential equation,…

Q: If A+ iB is Hermitian (A and Bare real) show that [ AB -BA] is symmetric.

A: As per the question we are given two real matrices A, B such that (A + iB) is Hermitian. Now we have…

Q: If n(B) = 210, n(A ∩ B ∩ C) = 55, n(A ∩ B ∩ CC) = 20, and n(AC ∩ B ∩ C) = 65, what is n(AC ∩ B ∩…

A:

Q: Find the value of the determinant D given by: b 3 d -4 a D= с 6 9 9 where a = 3, b = 4, c = 11, d =…

A:

Q: 1 √ [√6 +41 b) Evaluate the integral [²x sinh(4x)]dx. a) Solve the integral √6+4x-2x² dx using an…

A: The integrals are calculated as shown below.

Q: 7. An individual's utility function has the form U = x₁ x2, where xi and x2 are the quantities…

A: Quantity consumed of good 1= x1 Quantity consumed of good 2= x2

Q: • For the orthogonal set {1₂ Cos(x), Cos (2x),.. find its corresponding orthonormal set.

A: We have to find the orthonormal set of the given orthogonal set of vectors.

Q: Find the volume of the solid region Q bounded below by the upper nappe of the cone z2 = x2 + y2 and…

A: Given: The given region is bounded below by the upper nappe of cone z2=x2+y2 and bounded above by…

Q: 1 Problem 10: Consider the matrix B= 0 -2 1 (4) Find a basis for the null space of B. (5) Verify…

A:

Q: 4x² + 2√√3xy + 2y² = 1 ugh what angle should the axes be rotated so that the term xy e the…

A:

Q: The expression in Exercise 8.5.9 is called the Fej´er kernel and will be denotedby FN(θ). Analogous…

A: The Fejér kernel is a kernel used to express the effect of Cesaro summation on Fourier series and…

Q: 6) Solve the nonhomogeous equation y" + y² - 2y = xe ² explaining clearly each step.

A: Solution -  6  :  Given that The nonhomogeneous differential equation…

Q: Let R = ZOZO · · (the collection of all sequences of integers under componentwise addition and…

A: As per the question we are given a collection of integer subsequences as : R = ℤ ⊕ ℤ ⊕ ℤ ⊕ ... And…

Q: For the given function y(x) = - cos x² - In (1-x²) x" a) Find the Maclaurin series up to x inclusive…

A:

Q: Around 1910 , the Indian mathematician Srinivasa Ramanujan discovered the…

A: As per the question we are given the famous Ramanujan's π series and we have to show that the…

Q: the infinite region in the first quadrantbetween the curve y = e-x and the x-axis. Find the centroid…

A: Given curve is y=e-x. We have to find the centroid of the region.

Q: decide if the given statement is true or false,and give a brief justification for your answer.If…

A: As the Legendre's equation has two independent Frobenius series solutions we have to prove for both…

Q: Solve the following system by the method of reduction. -8z = 32 2x-3y-3z= 31 2x+2y-3z= 1 4x+2y + 2z…

A:

Q: 3. Let T be a linear operator in C² and is defined by T(a, b) = (3a + (2 + i)b, (2 – i)a + 7b) (a)…

A: :you have asked a question with more than 3 subparts (including 4 parts in (b)). Hence we solve (a)…

Q: The ABC Ink Company is a small family-owned company that sells packages of ink cartridge refills for…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…