
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Transcribed Image Text:9. Using eigenvalues, find the general solution to the following system of
equations.
x' = -6x + 4y
y' = -3x + y
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- This was incorrect last time I asked so I will try again, thank you!.arrow_forwardÿ' = -[3. a. Find the eigenvalues and eigenvectors for the coefficient matrix. i 3/1-1/16 5 5 A₁ = i = 1 • Find the real-valued solution to the initial value problem yí = ly/₂ = Use t as the independent variable in your answers. 31(t) = 11 y2(t) = -15 15 2 -5 -3 3y1 + 2y2, -5y1 - 3y2, y. and A₂ = -i 9 y₁ (0) = 11, Y2(0) = −15. 9 V2 = T 1 i 3/4 + 1/4 5 35arrow_forwardYou 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)äarrow_forward
- Apply the eigenvalue method to find a general solution of the given system. Use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system. x', = - 2x, + 8x2. x'2 = 12x, - 6x2 What is the general solution in matrix form? x(t) =Oarrow_forwardConsider the linear system dx₁ dt dx₂ dt = 4x1 - 3x₂ = 3x1 + 4x2. 1. Show that upon conversion to the form X'= AX, the eigenvalues of A are complex. 2. Find the general solution of the system.arrow_forward2. Consider the eigenvalue problem, y" + Ay = 0, for 0 < x < 7/2; y' (0) = 0, y(n/2) = 0. Find all eigenvalues and eigenfunctions for the case where the auxiliary equation has complex roots.arrow_forward
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