3. For the following systems with distinct real eigenvalues, find the general solutions:(a) x' = 4x + y, y' = 6x − y(b) x' = −50x + 20y, y'=100x - 60y

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Answered: 3. For the following systems with…

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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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
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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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3. For the following systems with distinct real eigenvalues, find the general solutions: (a) x' = 4x + y, y' = 6x - y (b) x' = −50x + 20y, y' = 100x - 60y