A differential equation and various initial conditions are specified. Sketch the graphs of the solutions satisfying these initial conditions. For each exercise, put all graphs on one pair of axes.
a. dy/dt=3y(y-2); y(0)=1; y(-2)= -1; y(0)=3; y(0)=2.
b. dy/dt=cos y; y(0)=0; y(-1)=1; y(0)= -pi/2; y(0)=pi.
c. dv/dt= -v2-2v-2; v(0)=0; v(1)=1; v(0)=1