Solve the following differential equation using both the method of trial functions and the method of variation of parameters d²y dy - 7y = e²x, with y(0) = 3 and y'(0) = 2. dr2 dr.

Q: Blue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the Hydro-Lux.…

A:

Q: A cable hangs between two poles of equal height and 30 feet apart. Set up a coordinate system where…

A: We have to find the length of the curve   for

Q: B -7 1.8 Let f(x) = { for 0 << 4, for 46. (a) Compute the Fourier cosine coefficients for f(z). ak…

A: Given Information:The piecewise function is given as:To find:a) The Fourier cosine series of the…

Q: Convert the following problem to standard form and solve: max x1 + 4x2 + x3  subject to 2x1 - 2x2 +…

A: see step 1

Q: Consider the second order linear differential equation z²y″(z) + zy′(z) + (z² − n²)y(z) = 0 - (4)…

A: (a) Given equation,z2y″+zy′+(z2−n2)y=0Rewrite the equation in the form y″+p(z)y′+q(z)y=0Then p(z)=1z…

Q: The graph of f(x) is shown (see figure). f(x) = 7x √x²+6 (a) Find the following limits. L = lim f(x)…

A: The function is given by .(a)And,

Q: . Let V and W be n-dimensional vector spaces, and let T: VW be a linear transformation. Suppose that…

A:

Q: Sales of tablet computers at Marika Gonzalez's electronics store in Washington, D.C., over the past…

A: The result by Excel QM is:a) Forecasted values are calculated by: FVi+1=α∗Di+(1−α)∗FViwhere FV is…

Q: Suppose that you just turned 2 5 years old and that you wish to receive a monthly ordinary annuity…

A:

Q: help me with a and b please. thank

A: For the given differential equation.For the given one of the solutions, find the other solution and…

Q: Consider the mathematical program below for the remaining questions: max 18x1 + 22x2 + 7x3 +14x4…

A: max s.t We have to verify  is valid inequality or not.

Q: 8. True or false: If f is analytic at each point of a closed contour I, then fr f(z) dz = 0. If true…

A: The objective of the question is to determine the validity of the statement: If a function f is…

Q: Prove that these relations on the set of all functions from Z to Z are equiva- lence relations.…

A:

Q: For the 2-periodic function f(t) = { 0≤t < 1, 1 < t < 2, which of the following statements is true…

A:

Q: 4. A metal fabrication shop has a single punch press. There are currently three parts that the shop…

A: Given dataPartAnnual Demand Set Up Cost Cost (per Unit)Production…

Q: d²x Consider the equation of simple harmonic motion considered in Example sheet 14: (1) + w²x = 0,…

A:

Q: A clamped cubic spline S(x) on the interval 0≤ x ≤ 2 is defined by S(x) S√(x) 0≤x≤1 = S₁(x) 1≤x≤2 If…

A: (s′(0))2+(s′(2))2=25+(b+2c+18)2Explanation:Step 1:Step 2:

Q: 7. Find T(t), N(t), and B(t) for r(t) = (t³ − 4t)ỉ + (5t² − 2)j

A:

Q: Convert the differential equation u"+2u'+5ue into a system of first order equations by letting x =…

A:

Q: Number 6 (b and d only!)

A: We have to find the invertible matrix Q

Q: Calculate the integral approximations Tg and Ms for fr³ dx. Your answers must be accurate to 8…

A: We will find the integral approximations T8 and M8.

Q: points are expressed in homogeneous coordinates). You want to uniformly scale point P2 by 1/2 and…

A: Given the points . These points are in homogeneous coordinates.(a)We want to perform the given…

Q: 5. Express in exponential form. a) log5 625 = 4 b) log16 4: = c) loga c = b 2

A:

Q: Reflexive. • Anti-reflexive. • Symmetric. • Anti-symmetric. Justify all your answers. Transitive. •…

A: Let's consider a few examples of elements inside the relation R, where (a,b)∈ R if and only if…

Q: = Let p¹²-2x+1, p² = 3 +3x+1 and p35x + 10. Let = x³-3x + 4. Is q in me span of pl,p2 and p3?

A:

Q: 3.1 In the diagram below is a graph of some of the terms of an arithmetic sequence. The graph…

A: To find the constant term d of an arithmetic sequence, we can use the formula:Tn=a+(n−1)dwhere:- Tn…

Q: For each of the differential equations, determine the complementary solution, and then use the…

A:

Q: what is written after 2xy - 2sin(y) in part i.

A:

Q: y 3. y'= ✓ {yln(y)-x=cy} x + y

A:

Q: Your company is evaluating the prospect of purchasing a new plant from a competitor. Because of the…

A: We have given: Rate, r0.07adjustment factor0.95Year, n123Cash inflow100000020000005000000To…

Q: In 2010, of a total of 67,000 rooms on the Las Vegas Strip, Caesars Entertainment managed 22,880,…

A: a) The launch of CityCenter and the Cosmopolitan would build the stock of lodgings in Las Vegas.…

Q: A certain kind of a ceramic tile has the form of a 4 × 4 board. Each of the 16 squares is colored…

A: Given:A certain kind of a ceramic tile has the form of a 4 × 4 board. Each of the 16 squares is…

Q: For the ODE xy" - 2y + 9x5y = 0, what is the resulting ODE for y(t) under the change of variables t…

A:

Q: Let A and B be subsets of a space X such that A is an open set and B is a closed set. Then a. A-B is…

A:

Q: Find the order and degree of the differential equation:- d³y d4y dy + dx3 = 6xy dx4 dx .

A: The objective of the question is to find the order and degree of the given differential equation:…

Q: Approximate √125 using the Babylonian technique.

A: we have, The first step in the Babylonian technique is to guess the given root value based on the…

Q: Consider the bilinear form H: R2 × R2 R defined by →> = x1 y1 + 6x1y2+6x2Y1 + 3x2Y2. H Let B= =…

A: Given the bilinear form  defined by.The ordered basis of R2 is .

Q: 3 Find the Fourier series expansion for the function -2< x < 0 0 < x <1, 0 f(x) = = X 2-x 1 < x < 2…

A:

Q: prove, that for subsequent follow-up reaction-intermediat applies: dCB ek₂t + K2CBеk₂t = (CB. ekzt)…

A:

Q: d³y Find the order and degree of the differential equation:- + dx3 d4y dx4 = = 2xy- dy dx .

A:

Q: 4. The vertical position, h, in metres, of a Ferris wheel is modeled using the function h(t) =…

A: The graphic representation of the given information is:This means that the Ferris wheel takes 40…

Q: Problem 13  find the general solution of the given second-order differential equation.  3y''+2y'+y=0

A:

Q: 1. Consider the conduction of heat in a rod 40 cm in length whose ends are maintained at 0°C for all…

A:

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS PLS

A:

Q: Choose the power series solution to y" - 4xy + (4x2 - 2)y = 0. ○ (ao + α1x)ex² O None a² ○ (a +…

A:

Q: A large container made to hold water has the equation z = 8 (x² + y²) 7/2 (The z-axis points up.)…

A: (a)Inagine a circular layer (green colour) of water at depth z.The radius of this circular disc is…

Q: Customers follow a Poisson process with arriving rate 6 per hour to arrive at a service center. The…

A:

Q: B = (1. x + 1,x² + x) forms an ordered basis for P3. Give the B-coordinate vector of each of File…

A:

Q: don't understand why it is An*r^-n + Bn*r^-n. Why is it r^-n and not r^n? Please let me know. Thank…

A:

Q: Sketch a graph of y = 3 sin(2x-л) + 2. List below 5 points of 1 cycle.

A: We shall use MATLAB to plot the given function. With this, the plot will be precise helping for your…