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Question: 2 (Small changes in initial condition) Consider the differential equation dy dr a). Find the general solution of the above DE. b). Solve the initial value problem dy =-(y-1)², y(0)=1.01. dz Find the largest interval where your solution is the solution of the IVP. c). Solve the initial value problem dy dr =-(y-1), y(0) = 1. Find the largest interval where your solution is the solution of the IVP. d). Solve the initial value problem dy --(y-1)², y(0) 0.99. Find the largest interval where your solution is the solution of the IVP? e). Show that solution of the IVP in part c) is the only constant solution (that is solution y such that y = a for all r ER). These solutions are called equilibrium solutions. Is it necessary to solve differential equation to find the equilibrium solutions? f). Describe the behaviour of solutions of parts b) and d) relative to the equilibrium solution as r grows. Use Matlab to plot solutions to all three IVPs above in one graph. Choose a large enough interval for r to demonstrate the difference in behaviours of solutions in parts b) and d). =-(-1)².