Let F(x, y) = (y,x). (This vector field also appears in Exercise 1.5.) (a) If a is a real number, show that a(t). (alet

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Let F X Y Y X This Vector Field Also Appears In Exercise 1 5 A If A Is A Real Number Show That A T Alet 1 (212.78 KiB) Viewed 36 times

Let F(x, y) = (y,x). (This vector field also appears in Exercise 1.5.) (a) If a is a real number, show that a(t). (alet tet), ale -- +)) and a(t) = (ale- e), ale +e-)) are integral paths of F. (b) Describe the integral curves, and sketch a representative sample of them. Indicate the direction in which the curves are traversed by the integral paths. (Hint: To find a relationship between 1 and y on the integral paths, compute r(t)” and y(t)2.)