comp2.html

> with(plots);
with(DEtools):

> DEplot(diff(y(t),t$2) + 0*diff(y(t),t) + 9*y(t) = 0, y(t), t = 0 .. 10, [[y(0) = 0, D(y)(0) = 0]], y=-2..2,stepsize=.05,title =`no damping, y(0) = 0, D(y) = 0`,linecolor=blue);

> DEplot(diff(y(t),t$2) + 0*diff(y(t),t) + 9*y(t) = 0, y(t), t = 0 .. 10, [[y(0) = 1, D(y)(0) = 0]], y=-2..2,stepsize=.05,title =`no damping, y(0) = 1, D(y) = 0`,linecolor=blue);

> DEplot(diff(y(t),t$2) + 0*diff(y(t),t) + 9*y(t) = 0, y(t), t = 0 .. 10, [[y(0) = -1, D(y)(0) = 0]], y=-2..2,stepsize=.05,title =`no damping, y(0) = 0, D(y) = 0`,linecolor=blue);

> DEplot(diff(y(t),t$2) + 0*diff(y(t),t) + 9*y(t) = 0, y(t), t = 0 .. 10, [[y(0) = 1, D(y)(0) = 5]], y=-2..2,stepsize=.05,title =`no damping, y(0) = 1, D(y) = 5`,linecolor=blue);

> DEplot(diff(y(t),t$2) + 1*diff(y(t),t) + 9*y(t) = 0, y(t), t = 0 .. 10, [[y(0) = 1, D(y)(0) = 0]], y=-2..2,stepsize=.05,title =`small damping, y(0) = 1, D(y) = 0`,linecolor=blue);

> DEplot(diff(y(t),t$2) + 3*diff(y(t),t) + 9*y(t) = 0, y(t), t = 0 .. 10, [[y(0) = 1, D(y)(0) = 0]], y=-1..1,stepsize=.05,title =`small damping, y(0) = 1, D(y) = 0`,linecolor=blue);

> DEplot(diff(y(t),t$2) + 3*diff(y(t),t) + 9*y(t) = 0, y(t), t = 8 .. 12, [[y(0) = 1, D(y)(0) = 0]], y=-0.000005..0.000005,stepsize=.05,title =`small damping, y(0) = 1, D(y) = 0`,linecolor=blue);

> DEplot(diff(y(t),t$2) + 6*diff(y(t),t) + 9*y(t) = 0, y(t), t = 0 .. 10, [[y(0) = 1, D(y)(0) = 5]], y=-1..2,stepsize=.05,title =`critical damping, y(0) = 1, D(y) = 5`,linecolor=blue);

> DEplot(diff(y(t),t$2) + 7*diff(y(t),t) + 9*y(t) = 0, y(t), t = 0 .. 10, [[y(0) = 1, D(y)(0) = 5]], y=-1..2,stepsize=.05,title =`over-damped, y(0) = 1, D(y) = 5`,linecolor=blue);

> DEplot(diff(y(t),t$2) + 7*diff(y(t),t) + 9*y(t) = 0, y(t), t = 0 .. 10, [[y(0) = -1, D(y)(0) = 5]], y=-1..0.5,stepsize=.05,title =`over-damped, y(0) = -1, D(y) = 5`,linecolor=blue);

> DEplot(diff(y(t),t$2) + 6*diff(y(t),t) + 9*y(t) = 0, y(t), t = 0 .. 10, [[y(0) = -1, D(y)(0) = 5]], y=-1..0.5,stepsize=.05,title =`critically damped, y(0) = -1, D(y) =5`,linecolor=blue);

> DEplot(diff(y(t),t$2) + 10*diff(y(t),t) + 9*y(t) = 0, y(t), t = 0 .. 10, [[y(0) = -1,D(y)(0) = 5]], y=-1..0.5,stepsize=.05,title =`over-damped, y(0) = -1, D(y) = 5`,linecolor=blue);