The cat command concatenates (in this case) a name and an integer to form a name.  See the help page ?cat.

The cat command concatenates (in this case) a name and an integer to form a name.  See the help page ?cat.

P[x] := v -> subs(m = v, S[cat(`x_`,floor(v))]);

P[y]:= v -> subs(m = v, S[cat(`y_`,floor(v))]);

P[x] := v -> subs(m = v, S[cat(`x_`,floor(v))]);

P[y]:= v -> subs(m = v, S[cat(`y_`,floor(v))]);

Actually it should work: I think the problem is just that list1 and its sublists have too few elements.  You seem to have

 list1:=[[1,2],[3,4]]

but you want i and j to go up to 3.  Try it with, say, list1 := [[1,2,3],[3,4,5],[4,5,6]].

Actually it should work: I think the problem is just that list1 and its sublists have too few elements.  You seem to have

 list1:=[[1,2],[3,4]]

but you want i and j to go up to 3.  Try it with, say, list1 := [[1,2,3],[3,4,5],[4,5,6]].

Yes, you do need the eigenvalues and eigenvectors.  The eigenvalues are the diagonal elements of D, and the eigenvectors are the columns of P.

Yes, you do need the eigenvalues and eigenvectors.  The eigenvalues are the diagonal elements of D, and the eigenvectors are the columns of P.

I agree that Maple's handling of 0^i may not be optimal, but I don't understand your complaint about 1^i.  When is the simplification of 1^i to 1 invalid?

I agree that Maple's handling of 0^i may not be optimal, but I don't understand your complaint about 1^i.  When is the simplification of 1^i to 1 invalid?

> with(DEtools):
> de:=diff(y(x) ,x) = 1+x*y(x)^2;
> DEplot(de, y(x), x=-2..2, y=-2..2, [[0,1.5],[0,-1.5],[0,0]], arrows=medium, linecolour=blue);

> with(DEtools):
> de:=diff(y(x) ,x) = 1+x*y(x)^2;
> DEplot(de, y(x), x=-2..2, y=-2..2, [[0,1.5],[0,-1.5],[0,0]], arrows=medium, linecolour=blue);

An integral curve is just a solution of the differential equation.  In order to specify one, you need initial values.  If the question doesn't specify them for you, you should choose some yourself.  Try to do it in such a way that you get a good selection of curves passing through all regions of the plot.

An integral curve is just a solution of the differential equation.  In order to specify one, you need initial values.  If the question doesn't specify them for you, you should choose some yourself.  Try to do it in such a way that you get a good selection of curves passing through all regions of the plot.

For example:

> with(plots):
   plotter:= evalf(Array(1..500, i -> [sin(i), sin(sqrt(2)*i),cos(sqrt(2)*i)]));
   display([seq(pointplot3d(plotter(1..10*j),symbol=solidbox),j=0..50)], insequence=true);