Question

(1 point) Consider the system of differential equations dx dt = -1.6x + 0.5y, dy dt = 2.5x – 3.6y. For this system, the smaller eigenvalue is -41/10 and the larger eigenvalue is -11/10 [Note-- you may want to view a phase plane plot (right click to open in a new window).] If y' Ay is a differential equation, how would the solution curves behave? All of the solutions curves would converge towards 0. (Stable node) All of the solution curves would run away from 0. (Unstable node) The solution curves would race towards zero and then veer away towards infinity. (Saddle) The solution curves converge to different points. The solution to the above differential equation with initial values x(0) = 6, y(0) = 4 is x(t) = y(t) =

Answer 1

du t 는 16ut osg =프리 아 글 5 dy y: g.su -30g t! U 18 anto g X'= AX where x- ㅠ [5] A= g S (A-11 ܟ ܐ ,; A+에 CO 100 베영 요 5 =) LrL (+) + loo (oo lou 다 -21 (o : -1 lo Sog Smaller eigen value is - - 41 10 and Larger eigen value is laa (1 lo 의

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