Question

differential equations

y(0)=3

Read each problem carefully. Show all your work. Turn off your phones. No calculators! X1. Consider the differential equation y' = -y(y + 1)(y-4). (a) (3 points) Find the equilibrium solution(s) (y = 0). (b) (3 points) Sketch the direction field. (4 points) Sketch the solution y(t) with initial condition y(0) = -1. Sketch another solution y(t) with initial condition y(a) = 3.

Answer 1

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5 Losll t 4 Loyt+ hey-10ntc Lugt-4)+ Lost-L5-r0tc t+1 7 Log 1d-4)Y1)| -Log1 915 - -ront omt (d-1)t -2n 5 at (-4))1 4 on t- FO at 13-4)4) 35 - x 256 243 256 24 3 (-1)-1t -2 -256 e 7.5 243

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