quiz6_Solution - initial condition in that interval...

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Math 242, Spring ?OLL 1. (3 + 3 f 4 points) (a) Solve the equation f(y): 0 to find the critical points of the autonomous differential equation: a' :16 - Y2 (b) Analyze the sign of f (y) t" determine whether each critical point is stable or unstable, and construct the corresponding phase diagram for the differential equation. (c) Sketch several solution curves of the differential equation. For each of the intervals determined by the critical points, have at least one solution curve with
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Unformatted text preview: initial condition in that interval. Drawings are not expected to be very precise but should illustrate the general tendencies. If any of the solution curves has a vertical or horizontal asymptote try to make that fact clear, annotating your drawing if necessary. (ri)\6.-f'o )rt=lG, 5'-t-l e< $:\ (b) :'=lrl 5'-\ 1 g. j=4 J gq *i (.r'J< , o, , n 'rol*1r)o,* \f ,7- al;uu.*" _l 9o{4.'tro^ P h"sn fit'3"-' . a t - *l(-q q unlah&. t+a,ble l.""to"'tnt htlthfto{" 'qL (.\...
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