Direction Fields and Solution Curves

> ode1 := diff( x(t), t ) = ? * x(t) + ? * y(t) ;

> ode2 := diff( y(t), t ) = ? * x(t) - ? * y(t);

> MODEL := { ode1, ode2 }:

>

> VARS := { x(t), y(t) }:

> DOMAIN := t=0.. ? :

> RANGE := x= ? .. ? , y=- ? .. ? :

> dirPLOT := DEplot( MODEL, VARS, DOMAIN, RANGE, arrows=MEDIUM ):

> dirPLOT;

>

> IC := [ [ x(0)= ? , y(0)= ? ], [ x(0)= ? , y(0)= ? ], [ x(0)= ? , y(0)= ? ]: # use more or fewer than 3 IC's as necessary

> solPLOT := DEplot( MODEL, VARS, DOMAIN, RANGE, IC, arrows=NONE, linecolor=GREEN ):

> #solPLOT;

>

> ICline := [ [ x(0)= ? , y(0)= ? ], [ x(0)= ? , y(0)= ? ],
[ x(0)= ? , y(0)= ? ], [ x(0)= ? , y(0)=- ? ] ]:

> linePLOT := DEplot( MODEL, VARS, DOMAIN, RANGE, ICline, arrows=NONE, linecolor=BLUE ):

> #linePLOT;

>

> display( [ dirPLOT, solPLOT, linePLOT ], title=` ??? ` ); # omit linePLOT for complex eigenvalues

>