1. (10 pts) Suppose that y(t) denotes the size of a population at time t. The predation reduces the size of the population so that the equation of the population is given by dtdy=2y1+yy a) (3 pts) Find the equilibrium points of the equation. b) (3pts) Sketch the phase line. c) (4 pts ) If y(0)=2 or y(0)=1/2, what are the asymptotical behavior of solutions as t, i.e. what are limy(t) ? 3. (20pts) Solve the differential equation by the integrating factors x2022y(x)+2022x2021y(x)=e7x,y(1)=0 4. (20 pts) Solve the initial value problem by separation of variables dtdy=2y+41,y(0)=5