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Take the conservative equation "+x²-4=0. Write down the corresponding first order system using the extra variable y: yhelp (formulas) y= | help (formulas) The critical points are on the x-axis at the following two x values (order them as they are on the number line): -2 2 help (numbers) Compute the Jacobian matrix for all x and y. help (formulas) help (matrices) The behavior at the first critical point is saddle The behavior at the second critical point is center Book: Section 8.2 of Notes on Diffy Qs

Take the conservative equation "+x²-4=0. Write down the corresponding first order system using the extra variable y: yhelp (formulas) y= | help (formulas) The critical points are on the x-axis at the following two x values (order them as they are on the number line): -2 2 help (numbers) Compute the Jacobian matrix for all x and y. help (formulas) help (matrices) The behavior at the first critical point is saddle The behavior at the second critical point is center Book: Section 8.2 of Notes on Diffy Qs

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter10: Systems Of Equations And Inequalities
Section10.CR: Chapter Review
Problem 5CC: What operations can be performed on a linear system to arrive at an equivalent system?
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Take the conservative equation "+x²-4=0. Write down the corresponding first order system using the extra variable y: yhelp (formulas) y= | help (formulas) The critical points are on the x-axis at the following two x values (order them as they are on the number line): -2 2 help (numbers) Compute the Jacobian matrix for all x and y. help (formulas) help (matrices) The behavior at the first critical point is saddle The behavior at the second critical point is center Book: Section 8.2 of Notes on Diffy Qs
Transcribed Image Text:Take the conservative equation "+x²-4=0. Write down the corresponding first order system using the extra variable y: yhelp (formulas) y= | help (formulas) The critical points are on the x-axis at the following two x values (order them as they are on the number line): -2 2 help (numbers) Compute the Jacobian matrix for all x and y. help (formulas) help (matrices) The behavior at the first critical point is saddle The behavior at the second critical point is center Book: Section 8.2 of Notes on Diffy Qs
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