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8. Consider the function -2r y = c₁e² cos 2x + c₂e² sin 2x + c3 + C₁x + c5е¯¯² + c6e- +c7xe-2x with the c, are arbitrary constants. This y is the general solution to a certain homogeneous linear first-order ODE. Which of the following is its auxiliary equation? (a) r²(1)(r-2)(r+1)(r+ 2)² = 0 (b) r²(r 1)² (r-2) (r + 1)²(r + 2)² = 0 (c) r²(r− 1)² (r² + 4)(r+1) (r + 2)² = 0 (d) r(r² - 2r+5)(r + 1)(r + 2)² = 0 (e) r²(r²2r+5) (r + 1) (r + 2)² = 0 ✓

8. Consider the function -2r y = c₁e² cos 2x + c₂e² sin 2x + c3 + C₁x + c5е¯¯² + c6e- +c7xe-2x with the c, are arbitrary constants. This y is the general solution to a certain homogeneous linear first-order ODE. Which of the following is its auxiliary equation? (a) r²(1)(r-2)(r+1)(r+ 2)² = 0 (b) r²(r 1)² (r-2) (r + 1)²(r + 2)² = 0 (c) r²(r− 1)² (r² + 4)(r+1) (r + 2)² = 0 (d) r(r² - 2r+5)(r + 1)(r + 2)² = 0 (e) r²(r²2r+5) (r + 1) (r + 2)² = 0 ✓

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.5: Solution Of Cubic And Quartic Equations By Formulas (optional)
Problem 29E
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8. Consider the function y = c₁e² cos 2x + c₂e sin 2x + c3 + C₁x + c5€¯ + c6е 2x (a) r²(r - 1)(r-2) (r + 1) (r + 2)² = 0 (b) r²(r 1)²(r - 2)(r + 1)² (r + 2)² = 0 (c) r²(r− 1)² (r² + 4)(r + 1)(r + 2)² = 0 (d) r(r² − 2r+5)(r + 1)(r + 2)² = 0 (e) r²(r² - 2r+5)(r+1)(r+ 2)² = 0 ✓ + C7xe -2x with the c, are arbitrary constants. This y is the general solution to a certain homogeneous linear first-order ODE. Which of the following is its auxiliary equation?
Transcribed Image Text:8. Consider the function y = c₁e² cos 2x + c₂e sin 2x + c3 + C₁x + c5€¯ + c6е 2x (a) r²(r - 1)(r-2) (r + 1) (r + 2)² = 0 (b) r²(r 1)²(r - 2)(r + 1)² (r + 2)² = 0 (c) r²(r− 1)² (r² + 4)(r + 1)(r + 2)² = 0 (d) r(r² − 2r+5)(r + 1)(r + 2)² = 0 (e) r²(r² - 2r+5)(r+1)(r+ 2)² = 0 ✓ + C7xe -2x with the c, are arbitrary constants. This y is the general solution to a certain homogeneous linear first-order ODE. Which of the following is its auxiliary equation?
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