minutes_928.mws
Thu Sep 29 15:35:07 MDT 2005

Minutes of our meeting, Wednesday, 9/28/05

>

restart;

>	with(plots, display, implicitplot):

>	with(plottools, disk):

>	with(DEtools, DEplot):

##################################################

>	DE1 := D(y)(t) = v(t):

>	DE2 := D(v)(t) = 2/3*y(t) - 5/3*v(t):

######################################################

>	SYS := [DE1, DE2]:

>	VARS := [y(t), v(t)]:

>

>	TRG := t=0..10:

>	YRG := y=-2..2:

>	VRG := v=-2..2:

>

>	PTS := [[1/3,-2/3], [-1/2,-1/6], [1/2,1/2], [0,2], [0,-2]]:

>

>	mkIC := u -> [y(0)=op(1,u), v(0)=op(2,u)]:

>	IC := map(mkIC, PTS):

>

>	P := DEplot(SYS,VARS,TRG,IC,YRG,VRG):

>

>	P := P,implicitplot( 2*y - 5*v = 0, YRG, VRG, colour=BLACK):

>

>	P := P, op(  map( t -> disk(t, 1/20, colour=BLACK), PTS)  ):

>

>	display([P]);

The plot shows the direction field as we doped out in class on Wednesday, 9/28/05.   The thin black line is the v'(t) = 0 line.   The black spots are the initial points of various solutions.  Note the two straight-line solutions.

>	######################################################

>

>