Hi there,

I have a 2-D ODE system. Objective: plot the nullclines and phase diagram around the equilibrium point. Problem: one of the ODEs has an integral and a call to DEtools[dfieldplot] returns:

Error, (in DEtools/dfieldplot) extra unknowns found

I have created a minimal example below.

> restart:
> with(plots):
#The Dynamic System
> xdot := diff(x(t),t) = x(t) - y(t) - 1;
   assume(x(t)>y(t)):
   ydot := diff(y(t),t) = y(t) - int(1/(x(t)+w)*y(t), w = y(t)-x(t) .. 2);
#Plotting the Null-Clines (ydot=0 and xdot=0)
> x1:=-1: x2:=5: y1:=-1: y2:=5:
   p1 := plot({x-1},x=x1..x2, colour=blue, thickness=3):
   p2 := plots[implicitplot](eval(rhs(ydot),{x(t)=x,y(t)=y}),x=x1..x2,y=1..y2, colour=brown, thickness=3, gridrefine=4):
   display({p1,p2});
Plotting the Phase Diagram
> FNS := {y(t),x(t)}:
   SYS := {ydot,xdot}:
   DEtools[dfieldplot](SYS, FNS, t=-1..1, scene=[x(t),y(t)], x=x1..x2, y=y1..y2); 
 

If I use the simpler expression below, the call to DEtools[dfieldplot] works. For instance, with:

> assume(x(t)>y(t)):
   assume(x(t)>0):
   ydot := diff(y(t),t) = y(t) - int(1/(x(t)+w)*y(t), w = -1 .. 2);

The problem seems to be not so much with the presence of the integral itself but with the presence of the variables x(t) and y(t) in the bounds of integration.

Any suggestions for a work-around will be welcome. Thanks.