@Rouben Rostamian  

actually i do not know which vector field can make it draw source and sink.

after search

http://www.maplesoft.com/support/help/Maple/view.aspx?path=plots/fieldplot3d

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

i choose vector field above

how to make it do not depend on t?

in equations, there are a(t), b(t) and c(t)

@Preben Alsholm 

i feel that the title is another question and goal, i ask in another post, if i add another link, it may be thought as duplicate post and being deleted.

@Kitonum 

if using 

https://en.wikipedia.org/wiki/Poincar%C3%A9%E2%80%93Hopf_theorem

to promise that there is sink and source, how to do?

i add sphere equation still can not see the arrow

ode1:=a(t)*(diff(a(t), t))+c(t)*(diff(c(t), t))=3*t:
ode2:=a(t)*(diff(a(t), t))+a(t)*(diff(a(t), t))*b(t)*(diff(b(t), t))*c(t)*(diff(c(t), t))=3*t:
ode3:=a(t)*(diff(a(t), t))+a(t)*(diff(a(t), t))*c(t)*(diff(c(t), t))+a(t)*(diff(a(t), t))*b(t)*(diff(b(t), t))*c(t)*(diff(c(t), t))=2*t:
subs({diff(a(t), t)=A,diff(b(t), t)=B,diff(c(t), t)=C}, {ode1,ode2,ode3}):
solve(%,{A,B,C});
allvalues(%);
Sys:=subs({A=diff(a(t), t),B=diff(b(t), t),C=diff(c(t), t),a(t)^2+b(t)^2+c^2(t)=1}%[1]);
DEtools[DEplot3d](Sys,[a(t),b(t),c(t)],t=0..3,a=0..3,b=0..3,c=0..3,[[a(1)=1,b(1)=2,c(1)=3]],scene=[a(t),b(t),c(t)], linecolor=red, axes=normal, orientation=[30,65]);

@Preben Alsholm 

i understandstand now, 

it has two system sys1 and sys2,

how to draw arrow diagram to see whether has sink or source?

@tomleslie 

i random select 3 boundary conditions

a(1) = 0, b(1) = 0, c(1) = 0

or

a(0) = 0, b(0) = 0, c(0) = 0

@Preben Alsholm 

how to plot 3 equations with 3 unknowns

a(t)*(diff(a(t), t))+c(t)*(diff(c(t), t))

a(t)*(diff(a(t), t))+a(t)*(diff(a(t), t))*b(t)*(diff(b(t), t))*c(t)*(diff(c(t), t))

a(t)*(diff(a(t), t))+a(t)*(diff(a(t), t))*c(t)*(diff(c(t), t))+a(t)*(diff(a(t), t))*b(t)*(diff(b(t), t))*c(t)*(diff(c(t), t))

@Preben Alsholm 

is there a systematic method to search initial condition automatically to apply it to all cases of system of differential equations in general?

i think your testing condition is one of step to terminate before looping.

If there is a good initial condition, I can just use above testing code to search the best differential ideal from thousands system.

moreover, I feel time variant solution has problem, in fact I search time invariant solution. This make me feel difficult to  think application of system.

@Preben Alsholm 

i choose one or zero. I do not know roots without solve. which roots allowed to choose?

which initial conditions are suitable for system which in a(t)*diff(a(t),t) form 's system?

@Kitonum 

actually i doing this kind of combination

http://stackoverflow.com/questions/32055730/exception-prelude-index-too-large-error

i meet difficulty in haskell, hope to do similar and better things in maple

@Rouben Rostamian  

originally i do it in F# and Haskell, but i feel that maple is more convenient , but i do not know how to make a combination of tree to archieve this.

I would like to search and validate a definition satisfy eeval1, eeval2, eeval3, eeval4 and print the result definitions

If I define f, it could be x+y, x*y, and g could be x+y, x*y and run through a combinations of them, which can have 4 combinations if the each possible definition satisfy four combinations, then it is true definition

Current MA and MB function can only be as a operator + and *, and have redundant combinations such as some do not have both MA and MB

eeval1 :: Mree Double -> Double
eeval1 (Meaf x)= x
eeval1 (Mode l And r)= eeval1 l * eeval1 r
eeval1 (Mode l Or r)= eeval1 l + eeval1 r
eeval1 (Mode l MA r)= eeval1 l + eeval1 r
eeval1 (Mode l MB r)= eeval1 l + eeval1 r

eeval2 :: Mree Double -> Double
eeval2 (Meaf x)= x
eeval2 (Mode l And r)= eeval2 l * eeval2 r
eeval2 (Mode l Or r)= eeval2 l + eeval2 r
eeval2 (Mode l MA r)= eeval2 l + eeval2 r
eeval2 (Mode l MB r)= eeval2 l * eeval2 r

eeval3 :: Mree Double -> Double
eeval3 (Meaf x)= x
eeval3 (Mode l And r)= eeval3 l * eeval3 r
eeval3 (Mode l Or r)= eeval3 l + eeval3 r
eeval3 (Mode l MA r)= eeval3 l * eeval3 r
eeval3 (Mode l MB r)= eeval3 l + eeval3 r

eeval4 :: Mree Double -> Double
eeval4 (Meaf x)= x
eeval4 (Mode l And r)= eeval4 l * eeval4 r
eeval4 (Mode l Or r)= eeval4 l + eeval4 r
eeval4 (Mode l MA r)= eeval4 l * eeval4 r
eeval4 (Mode l MB r)= eeval4 l * eeval4 r

@Christopher2222 

i guess that i need to reinstall maple 18 , before that i install maple sim 7.01

@Markiyan Hirnyk 

i just restart maple 18 again and paste code to clean console.

Please see my real case.

https://drive.google.com/file/d/0Bxs_ao6uuBDUcDFiQVRmcHBJeXM/view?usp=sharing

@Markiyan Hirnyk 

i use the upgrade file of 7.01 in my installation folder after upgrade to 7.01

still have the same error when do simulation

then i download the 3 files in the official web.

i can not upgrade again because it has already been upgraded.

is there any difference between old upgrade file and the upgrade file in official web?

do i need to uninstall maple sim 7.01 and install again?

@Markiyan Hirnyk 

maple sim 7

@Preben Alsholm 

actually i I am searching calabI yau equation from all combinations, but it seems need a*diff(,a)