Given the correct eigenvalues above and the eigenvectors below, what isthe general solution of the system:dx1= 2x yK₁ = ( ²¹₁ ) K² = ( 9 ) + + - ² +dtdy= -XdtX = 4₁₂ (²¹) e² + ²₂ (1) e²O Ax=₂(₁) +(¹₁)te+ (¹)et]O CX = G₁₂ (¹₁) e¹ + ₁₂ (¹₁) e² + (e¹]OBX = G(²¹) e² + a₂ (²¹) ²C₁O D

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Answered: Given the correct eigenvalues above and…

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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a. Find the eigenvalues and eigenvectors of the matrix x₁ (t) x₂ (t) = X₁ b. Solve the system of differential equations a' = = = V₁ = [₁ 5 -3 4 -2 and X₂ = satisfying the initial conditions V₂ = [₁8] =[3]
The options for matching the values of c1 and c2 are -4 through 1.
Use the eigenvalue method to find the solution of the following system with given initial conditions. x₁ = x₁, x₂ = -8x₁ — 4x2; x₁ (0) = −2, x₂ (0) = 3. Evaluate the solution at t = 1 and select the most approximate values. (1) ° [2] = [0.958] (1). 0.446 0.027 °[2()] = [73] (1). 0.673 [2] = O [1(1)] [x₂ (1) [0.043 0.776 = 0.033 0.561
You are solving a 2x2 system of the form : y' = PỶ + where P has constant entries with real different eigenvalues. Decide which of the following statements is correct: I can find a particular solution using the undetermined coefficients method with a try function of the form Y(t) = sin(t)å + cos(t)b I can find a particular solution using the undetermined coefficients method with a try function of the form Y(t) = (cos(t) + sin(t))ā I can only find the general solution for this problems using the Variation of Parameters method. Undetermined Coefficients won't work in this case. I can find the general solution using the undetermined coefficients method. To find the particular solution I should use a with a try function of the form Y(t) = sin(t)ä
1. For the system below, find the general solution, sketch the trajectories, being careful to include the eigenvector directions, and classify the type of fixed point: x = x, ÿ y = 2x - 5y.
) Consider the linear system X₁ = Y a. Find the eigenvalues and eigenvectors for the coefficient matrix. 18 v1 = b. Find the real-valued solution to the initial value problem {{{ = -3 -2 5 -3] Use t as the independent variable in your answers. y₁ (t) Y₂ (t) - 3y1 - 2y2, 5y1 + 3y2, y." , and X₂ = V2 y₁ (0) = 9, Y₂ (0) = -10. ||
Suppose that a 2 x 2 matrix A with real entries has an eigenvalue X = 1 + 3i with corresponding 4 i [12] eigenvector 1 + 2i Which of the following is NOT a solution of the linear system y' = Ay? y(t) = et y(t) = et y(t) = et y(t) = et 4 cos(3t) sin(3t) [cos(3t) + 2 sin(3t). 4 cos(3t) + sin(3t) cos(3t) 2 sin (3t) - cos(3t) + 4 sin(3t) 2 cos(3t) + sin(3t) cos (3t) - 4 sin (3t) -2 cos(3t) - sin(3t)
I already know the eigenvalues are -2+6i, and 2-6i, and the eigenvector is [6i,1] , and [-6i,1], im just struggling finding the overall solution
in pic
Find the General Solution of the given systems. Make sure to indicate your Eigenvalues and Eigenvectors.
Everything we've done with systems of 2 linear, constant co- efficient, homogeneous differential equations works for larger systems as well. Ask wolframalpha.com for the eigenvalues and eigenvectors of the following system of three differential equations, and use the result to write the general solution: -2 -4 2 *m-Biss X' (t) -2 1 2 X(t) 4 2 5 =
dy dy +3 dr? 6. Consider the second-order equation - 10y = 0. di (a) Convert the equation to a first-order, linear system. (b) Compute the eigenvalues and eigenvectors of the system. (c) For each eigenvalue, pick an associated eigenvector V, and determine the solution Y(t) to the system. (d) Compare the results of your calculation with the results that you obtained when you used the guess-and-test method in Homework 6, question 4.

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