This is the example I did in class Oct 7. Recall that we solved y''-2by'+y=0, y(0)=1, y'(0)=0, with -2 <= b <= 2. I used Maple.

> with(DEtools):with(plots):

> dsolve({diff(y(t),t$2)-2*b*diff(y(t),t)+y(t)=0,y(0)=1,D(y)(0)=0},y(t));

>animate(-1/2*(b-sqrt(b^2-1))*exp((b+sqrt((b-1)*(b+1)))*t)/(sqrt(b^2-1))+ 1/2*(b+sqrt(b^2-1))*exp((b-sqrt((b-1)*(b+1)))*t)/(sqrt(b^2-1)), t=0..10,b=-2..2,view=-5..5,frames=100,thickness=2, color=blue);