One Dimensional Plot of Solutionsrestart:
with(plots):
with(DEtools):Define the differential equation using parameters:
For a different equation, you will have to change the ODE.r:= 1; K:= 1;
ODE := [diff(x(t),t) = r*x(t)*(K-x(t))/K];Next pick the initial conditions which show the important features of the equation.IC:=[[x(0)=2],[x(0)=1],[x(0)=0.1],[x(0)=0],[x(0)=-0.1]];Plot t versus x.
Note: for a different ODE, you will probably have to change the range of x displayed.
(Here the range is from -1 to 2.) trajectplot :=DEplot(ODE, [x(t)], t=0..5,
IC,linecolour=BLUE, x=-1..2, stepsize=0.1,
arrows=NONE, method=classical[rk4],scene=[t,x]):
display(trajectplot);Plot the vector field for T' =1 and x' = r x(K-x)/Kvfplot := fieldplot([1,r*x*(K-x)/K], T=0..5, x = -1..2):
display(vfplot);display(trajectplot,vfplot);