Find a fundamental matrix of the following system, and then apply x(t) = Þ(t)Þ(0)¯¯ 1x to find a solution satisfying the initial conditions.x' =-5 -2|x, x(0)=25 51- 5t5eA. (t)=- 5t-2e-2e5t- 5t5eB. (t):2 cos 5t- 2 sin 5t- 5 cos 5t + 5 sin 5t 5 cos 5t + 5 sin 5tO© C. (t)=5 cos 5t 2 sin 5t - 2 cos 5t2 sin 5t + 5 cos 5t- 5 sin 5t5+2tO D. (t) =1-2e-5t1+2t -5-2e5tFind a solution satisfying the given initial condition.x(t) = ☐(Use integers or fractions for any numbers in the expression.)...

Answered: Find a fundamental matrix of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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I need the solution for part e
(a) Put the system x" + y' – 2y = 1, x" + y' – x – y = 2 in operator matrix form. (b) Use the operational determinant to obtain two ODES. (c) Solve for x and y.
Let p(x) = 5x + 4x³ + 3x² + 2x + 1 and [0 1 0 0 0 0 1 0 0001 0000 A = Find the matrix p(A). What is the determinant of p(A)?
I need the answer as soon as possible
Please help me.
Question 16 Suppose that you have downloaded data on the daily share prices for a company for the period from the start of 2020 to the end of 2020 from the website of Yahoo Finance UK. You have also calculated the daily rates of return for the company's shares as (closing price - opening price)/opening price. By using the knowledge that you have gained from descriptive statistics, how can you obtain useful information about the company's share performance in terms of risk and return using a range of alternative indicators? Note that you should give necessary formulas for the technical concepts wherever they may apply.
Consider the nonhomogeneous system: 1 2 4et -4 3 2e* a. Write a fundamental matrix for the associated homogeneous system 1 1 - cos (21) - sin 21 A cos (2t) 2 X = 1 cos 21 - sin 21 2 cos (21) b. Compute the inverse of X. X-1 c. Multiply by the nonhomogenity g(t) and integrate. 1/2
Consider a system of differential equations which has the general solution: 18]- = C, · cos (5. t) – sin (5 - t) )+C2 · sin (5 - t) + • Cos (5 - t (a) Determine the fundamental matrix (t) which has the property (0) = I. (t) = (b) Use the fundamental matrix found in part (a) to quickly determine the particular solution for the following initial conditions: r (t) : y (t) = :8]-[- (0): 1 (ii) r (t) = y (t) =
[101] Find the inverse of the matrix C = 01 1 using L2 1 4] cofactors. Show all your work.

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