Question:DEplot losses slope line when changing the ode's

Question:DEplot losses slope line when changing the ode's

Maple 2024

I am plotting phase plot of two first order ode's.

I noticed when added +t to one ode, the plot generated losses all the slope fields. Any one knows why and if this is just limitation of DEplot or if there is a way to workaround it.

THis worksheet has first example showing expected output, then second example where +t was added first ode. Now same code generates plot will all the slope field gone.

 > interface(version);

 > sys:=[diff(x(t),t)+diff(y(t),t) = x(t)+y(t), 2*diff(x(t),t)+diff(y(t),t) = 2*x(t)+3*y(t)]; DEtools:-DEplot(sys,[x(t), y(t)],         t = 0 .. 200,x = -1000 .. 1000,y = -1000 .. 1000,         [[x(0)=1, y(0)=2]],         labels = [x(t), y(t)],         linecolor =red,arrowsize = 1.5,axes = boxed,         color = 'magnitude[legacy]')

 > #added +t to the RHS of one ode. Everything else the same. sys_2:=[diff(x(t),t)+diff(y(t),t) = x(t)+y(t)+t, 2*diff(x(t),t)+diff(y(t),t) = 2*x(t)+3*y(t)]; DEtools:-DEplot(sys_2,[x(t), y(t)],         t = 0 .. 200,x = -1000 .. 1000,y = -1000 .. 1000,         [[x(0)=1, y(0)=2]],         labels = [x(t), y(t)],         linecolor =red,arrowsize = 1.5,axes = boxed,         color = 'magnitude[legacy]')

 > dsolve([op(sys),x(0)=1, y(0)=2]);

 > dsolve([op(sys_2),x(0)=1, y(0)=2]);

 >

update

if someone is interested, I found Maple has builtin function to check if system of ode's is autonomous or not. So changed my code to check first. Here is how to check:

 > interface(version);

 > restart;
 > sys:=[diff(x(t),t)+diff(y(t),t) = x(t)+y(t), 2*diff(x(t),t)+diff(y(t),t) = 2*x(t)+3*y(t)]; if DEtools:-autonomous(sys,[x(t),y(t)],t) then     DEtools:-DEplot(sys,[x(t), y(t)],         t = 0 .. 200,x = -1000 .. 1000,y = -1000 .. 1000,         [[x(0)=1, y(0)=2]],         labels = [x(t), y(t)],         linecolor =red,arrowsize = 1.5,axes = boxed,         color = 'magnitude[legacy]'); else   print("WARNING, non-autonomous system. Will not do phase plot"); fi;

 > #added +t to the RHS of one ode. Everything else the same. sys_2:=[diff(x(t),t)+diff(y(t),t) = x(t)+y(t)+t, 2*diff(x(t),t)+diff(y(t),t) = 2*x(t)+3*y(t)]; if DEtools:-autonomous(sys_2,[x(t),y(t)],t) then    DEtools:-DEplot(sys_2,[x(t), y(t)],         t = 0 .. 200,x = -1000 .. 1000,y = -1000 .. 1000,         [[x(0)=1, y(0)=2]],         labels = [x(t), y(t)],         linecolor =red,arrowsize = 1.5,axes = boxed,         color = 'magnitude[legacy]'); else   print("WARNING, non-autonomous system. Will not do phase plot"); fi;

 >