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I would like to understand this exercise I don't get the -0.4429 Page 4 5. Consider the ODE y' = (e - 1)(y + 1).

I would like to understand this exercise I don't get the -0.4429

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Page 4 5. Consider the ODE y' = (e - 1)(y + 1). (a) Sketch the graph of f(y) versus y (phase plot) and find the equilibrium solution(s). y = fly ) y'= 0 2 . ey- 1 = 0 => e'=1=> y= lil = 0 or y+ 1 = 0 - Y = - 1 + equilibrium solutions : y=-1, y = o 1-0 (b) For each equilibrium solution from part (a), decide whether it's stable, unstable, or semi- stable. Fully justify your answers. y' 70 for yc- 1 = y T toward y= -1 there. y = -) is a stable y'so for - kyco=> y'+ toward y= -1 there equilibrium y' y'd away from y= 0 there ] y = 0 is an y's0 for you =y'l away from y=0 there. unstable equilibrium (c) Draw the phase line and sketch several graphs of solutions in the ty-plane. -0.4429 y= fly) fly) y" = fly fly ) y y O + -0.4429 IP _ _ _ - - IP IP

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