Sample calculation (Text exercise 1.3.7):
  defining a differential equation
  constant solutions
  particular solution to the IVP
  plot direction field and solution curves
> restart;
> with(DEtools):
> de1 := diff(y(t),t) = y(t)*(y(t)-a)*(b-y(t));

                    d
             de1 := -- y(t) = y(t) (y(t) - a) (b - y(t))
                    dt

> a := 1; b := 2;

                                a := 1


                                b := 2

> const := [solve(y(t)*(y(t)-a)*(b-y(t))=0, y(t))];

                          const := [0, 1, 2]

> y2    := const(2);

                           y2 := [0, 1, 2]

> simplify(subs(y(t)=y2,de1));

      d
      -- [0, 1, 2] = [0, 1, 2] ([0, 1, 2] - 1) (2 + [0, -1, -2])
      dt

> ic := y(0) = (a+b)/2;

                           ic := y(0) = 3/2

> partsol := simplify(dsolve({de1,ic},y(t)));

                        I exp(t) sqrt(3) + sqrt(-9 - 3 exp(2 t))
      partsol := y(t) = ----------------------------------------
                                                   1/2
                                  (-9 - 3 exp(2 t))

> subs(partsol,ic);

                              y(0) = 3/2

> simplify(subs(partsol,de1));

                1/2                  1/2
     -I exp(t) 3    (-9 - 3 exp(2 t))           -3 I exp(t)
     ----------------------------------- = ---------------------
                             2                             3 1/2
               (3 + exp(2 t))              (-(3 + exp(2 t)) )

> DEplot(de1,y(t),t=0..4,{[0,3],[0,1.5],[0,.5],[0,.9],[0,-.1]},title='de1', 
  axesfont=[TIMES,BOLD,10],titlefont=[TIMES,BOLD,14],
  labelfont=[HELVETICA,BOLD,12], arrows=THIN,linecolor=blue,y=-1..4);

> 
>