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Consider the system dx dt = x + y dy dt = y. (a) Show that

Differential Equations 00 | 4th Edition | ISBN: 9780495561989 | Authors: Paul (Paul Blanchard) Blanchard, Robert L. Devaney, Glen R. Hall ISBN: 9780495561989 199

Solution for problem 1 Chapter 2.6

Differential Equations 00 | 4th Edition

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Differential Equations 00 | 4th Edition | ISBN: 9780495561989 | Authors: Paul (Paul Blanchard) Blanchard, Robert L. Devaney, Glen R. Hall

Differential Equations 00 | 4th Edition

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Problem 1

Consider the system dx dt = x + y dy dt = y. (a) Show that the x-axis consists of three solution curves. (b) Using HPGSystemSolver, sketch the solution curves for a number of initial conditions above and below the x-axis. Do these curve intersect the x-axis? Do they touch the origin? Justify your assertions.

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Review of Monday: Karyotype- Trisomy 21 Down Syndrome Kayrotpe with an extra chromosome 21 25% of cases it’s from the sperm, 75% it’s from the egg (the extra chromosome is coming from) As women get older they are more likely to have a child with Trisomy 21, while males don’t matter. Nondisjunction A Pair of Homologous Chromosomes go through normal meiosis 1, and then one set goes through normal meiosis 2, and the other set goes through nondisjunction where the two chromosomes are supposed to split, but they don’t. So the Eggs from the normal side then have 23 as they’re supposed to, and one egg that has an estra (24) and one that has one less (22). Meaning if they were all fertilized, the normal ones would have (46), the one with the extra would have (47), and the last would be missing one (45). When a baby girl is born, all her eggs are already started, and have doubled her chromosomes. This is why we think that when women get older the baby is more likely to have a baby with Trisomy 21 because the eggs are getting older. Sperm only lasts up to three months, which is the most commonly accepted reason why the age of a man has no contributing factor to an extra or lack of chromosome. Chromosome set #23 Females (XX) Male (XY) Female eggs have X Sperm gives X or Y Sperm determines the gender of the baby XXY Klinefelter Syndrome occurs in 1:800 births. Considered a biological male because of the Y, if there is a Y it is a male, no Y means female. Usually Sterile Usually Tall Underdeveloped Genitals XXY Criminal Syndrome Started in the 1960’s: Observation: Males are more aggressive than females. Question: Why Hypothesis: Y Chromosomes >>YY= really, really aggressive Data: Some extremely violent criminals were XYY. Lacked a control group. Turns out that the population of criminals with the extra Y is the same as the general population. Happens 1:1000 male births Tall Able to Reproduce XXX Super Females Irregular periods Used to have problems getting pregnant, but not anymore. Chromosome Set #23 Monosomy Only none lethal monosomy Only possible one to survive is X. Called Turner Syndrome. 1:2500 females Usually never menstruate (no children)

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Chapter 2.6, Problem 1 is Solved
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Textbook: Differential Equations 00
Edition: 4
Author: Paul (Paul Blanchard) Blanchard, Robert L. Devaney, Glen R. Hall
ISBN: 9780495561989

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Consider the system dx dt = x + y dy dt = y. (a) Show that