@Adri van der Meer 

i would like to plot a surface which lie on the two axis

this is the first step,

actually i am trying to find one equation which represent rectangle which can be plotted in 3d in maple

i do not know whether need two or more equations to draw 3d

i just hope to find one equation representing one 3d rectangle

i follow the steps to make a surface equation, but it is a surface without boundary,

any more needed to draw a rectangle?

@tomleslie 

sys satisfy some properties, the equations are correct.

@Preben Alsholm 

yes,

your commands result in correct answer , before that i have to manually change t(t) to t

dsol2:=`union`(dsol[]);
eval(eq2,dsol2);

purpose is for beautiful

@vv 

succeed to use your method to subs twice, it eliminiate the constant term. thanks

@Thomas Richard 

yes, after transformation, it become capital P and capital Q

@Carl Love 

my maple code sent a few hours ago, have you ever received it?

it may need cloud computing or super computer to run as my computer run slow and still have not finished running after one hour.

you can run for half an hour and then terminate it manually, then it has already been enough to see that

there is -n in result

@Carl Love 

it is highly secret, originally i want to encrypt it with zip file and send to you,

but it do not have attachment, hope maple prime web site do not save the message.

if so, please delete it in database.

@Carl Love 

i can send email to you, what is your email ?

@Carl Love 

it appear at

f := a*b*d - b;

[2,n,1,0]

subs(a=2,subs(b=n, subs(c=1, subs(d=0, f))))

i use maple 18

@Carl Love 

my worksheet has my latest invent part

i can only post part of it

varslist := indets(f6):
for kk from 1 to nops(setofnumbers) do
f7 := f6:
for jj from 1 to nops(varslist) do
f7:=subs(varslist[jj]=setofnumbers[kk][jj],f7):
od:
f7 := eval(simplify(expand(f7))):
if f7 - n = 0 then
if not assigned(masha[setofnumbers[kk]]) then
#print(f6):
masha[setofnumbers[kk]] := [f6]:
else
#print(f6):
masha[setofnumbers[kk]] := [op(masha[setofnumbers[kk]]), f6]:
end if:
end if:
od:

@Carl Love 

i seldom to use this command, so I do not have memory about it

@Rouben Rostamian  

i succeed to plot arrow in this way, is there any thing wrong with the 

concept in code?

actually i feel 2d is more easy to read rather than really plot on sphere

but i expect the concept of equations on sphere rather than draw arrow on sphere, that means after transform equations that can be expressed on sphere, the equations plot on 2d

rule_surf can only have two variables, is there 3 variables version

or should i view 3 times 2d diagram 

first time = a(t), b(t)

second time = a(t), c(t)

third time = b(t), c(t)

rulesol2d := rule_surf(<rhs(dsol[1][1]) | rhs(dsol[2][1])>,<0|1>);

rulesol2d := rule_surf(<rhs(dsol[1][1]) | rhs(dsol[3][1])>,<0|1>);

rulesol2d := rule_surf(<rhs(dsol[2][1]) | rhs(dsol[3][1])>,<0|1>);

rule_surf:=proc(beta,delta)
simplify(beta+v*delta,symbolic);
end:

ics := a(1)=0, b(1)=0, c(1)=0;
dsol := dsolve({ode1, ode2, ode3, ics});

with(VectorCalculus):
rulesol2d := rule_surf(<rhs(dsol[1][1]) | rhs(dsol[2][1])>,<0|1>);
fieldplot(rulesol2d, t=-1..1, v=-1..1,arrows=THICK);
rulesol3d := rule_surf(<rhs(dsol[1][1]) | rhs(dsol[2][1]) | rhs(dsol[3][1])>,<0|1|1>);
fieldplot3d(rulesol3d, t=0..1, v=0..1, a=0..1);

but this code only draw source, 

which situation it has sink ?

which situation it has source?

@Rouben Rostamian  

yes, this is the way.

if this example can use with my system in original question, it would be the best.

i guess that need to use

rule_surf(<a(t)|b(t),c(t)>,<0|1|1>

@Rouben Rostamian  

i stick to my original system,

searched a possible method is

rule_surf:=proc(beta,delta)
simplify(beta+v*delta,symbolic);
end:

rule_surf(<a(t)|b(t),c(t)>,<0|1|1>)

after solve for the result a(t) b(t) and c(t) in terms of t, there will be only one variable t

then use rule_surf to add a extra variable v to it, but i do not understand how to define delta.

then i use example below, but it only draw line on sphere, how to draw arrow on sphere?

cu:=tubeplot(convert(<a(t)|b(t)|c(t)>), t=O..2*Pi,radius=O.015,color=black,
numpoints=200,scaling=constrained):
spherel:=plot3d«cos(u)*cos(v) I sin(u)*cos(v) ISin(v»,
u=O .. 2*Pi,v=-Pi/2 .. Pi/2):

display({cu,spherel},style=wireframe, scaling=
constrained,shading=XYZ,lightmodel=light3,
orientation=[38,43]);

display({cu,spherel},scaling=constrained,
shading=XYZ,lightmodel=light3,orientation=[38,43]);

i do not have maple in my computer in office now, i may need to try at home. if you have maple, could you plot the diagram and post here?

the above code i reference from 

Differential Geometry and its Applications (Classroom Resource Materials) (Mathematical Association of America Textbooks)
John Oprea

what i want to do is draw arrow diagram to see whether have sink and source and then draw poincare section to see whether there is tangle and draw horse shoe. 

final goal is to create tangle with system

@Rouben Rostamian  

http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/lecture-notes/MIT18_03S10_c37.pdf

i read

u'(t) = F(u(t)) , F(x,y) = [ f(x,y) ; g(x,y) ]

it seems more complicated when think with my example. does it mean that dsolve({ode1, ode2, ode3}, a(t), b(t), c(t));

then [a(t), b(t), c(t)] is the vector field? but how do it use with sphere?

use

r = sqrt(a^2+b^2+c^2);
fld := [a/r,b/r,c/r];

how to use with original equations to plot arrow diagram?

should i remove (t) in coefficient of diff(...), in a(t) , b(t) and c(t)

ode1:=a*(diff(a(t), t))+c*(diff(c(t), t))=3*t:

ode2:=a*(diff(a(t), t))+a*(diff(a(t), t))*b*(diff(b(t), t))*c*(diff(c(t), t))=3*t:

ode3:=a*(diff(a(t), t))+a*(diff(a(t), t))*c*(diff(c(t), t))+a*(diff(a(t), t))*b*(diff(b(t), t))*c*(diff(c(t), t))=2*t:

smooth vector field on a sphere having sources or sinks

i guess that after dsolve ode1 ode2 ode3 and then substitute a(t), b(t) and c(t) into sphere

 i see that Kitonum solve result in terms of t,  it seems impossible to remove t from

r = sqrt(a(t)^2+b(t)^2+c(t)^2);
fld := [a(t)/r,b(t)/r,c(t)/r];

if i do not see t as time, i see t as data, can i see t as independant variable instead of dependant variable in vector field?

 but, if do this, there will be only one variables in vector field, it seems not enought to draw 2d or 3d arrow diagram

if need to maintain a,b,c, i think that after solve for a(t), b(t) and c(t) in terms of t, then solve t in terms of a(t), solve t in terms of b(t) and solve t in terms of c(t), there will be 3 kinds of solutions in terms of a(t), b(t), c(t).