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6. For y, = y3 _ y, y(0) = 30, -00 <30 < 00, draw the graph of (y) = y3-y versus y, determine the equilibrium solutions (critical points) and classify each one as unstable or asymptotically stable. Draw the phase line, and sketch several representative integral curves (graphs of solutions) in the (t, y) plane. Hint: None of this requires explicit formulas for solutions y = φ(t) of the initial value problem.] Using Differential Equations.

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graph of f (x)-x3-x is as shown below equibrium solutions are , y-0,1.-1 if y<.1 then f(y) <0 if -Icy<0 then f (y) >0 if 0<yc

9 10-9-8 -7 -6 5-4 -3 -21 /101 2 3 4 5 6 7 8 9 10 -4 -6 -8 -10

-3 -2 -1 -3

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