5. The slope field for the systemdx= 2x + 6ydtD.dy= 2x – 2ydtB.is shown to the right. The eigenvalues of the coefficient matrix are found to bed1 = 4 and A2 = -4 and their corresponding eigenvectors are V1 = (3, 1) andV2 = (1, –1), respectively.C(a) Determine the type of the equilibrium point at the origin.(b) Calculate all straight-line solutions.(c) Plot the x(t)- and y(t)-graphs for t > 0 for the ICs: B = (3, 1).

Given differential equations are, dxdt=2x+6ydydt=2x-2y Their eigenvalues are λ1=4 and λ2=-4 And the…

Answered: The slope field for the system da = 2x…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Suppose A is a 3 x 3 matrix with eigenvectors [1] V1 = V2 = 1 and v3 = corresponding to eigenvalues A1 =-, d2 = }, and A3 = 1, respectively. Find A and A20.
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Express the given system of higher-order differential equations as a matrix system in normal form. x" + 6x + 7y=0 y" - 2x=0 Which of the following sets of definitions allows the given system to be written as an equivalent system in normal form using only the new variables? OA. X₁ = x¹, x₂ = y' O B. X₁ =X, X2₂=X'', X3 = Y, X4 =y" O c. x₁ = x¹, x₂ = x¹, X3 = y', X4 =y" O D. x₁ = x, X₂ = x', X3 = Y, X4 = y' Write the system of equations using matrix notation. Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) OA. B. X₁ X₂ X₁ S w X4 || X₁ X2 x1 3 ... W X4 ро
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The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the eigenvalue method to find a general solution of the system. x', = 4x, + 2x2 + 2x3, x'2 = - 6x, - 4x2 - 2x3, x'3 = 6x, + 6x2 + 4x3 What is the general solution in matrix form? x(t) =

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