@Axel Vogt please update your post with maple code.

i think u are asking this question for the other main problem,right ? could u tell us your main problem ? if i understand your major problem,maybe u should look at this also :

http://www.mapleprimes.com/questions/151261-Problem-With-Collect

Good luck .

@acer thank u. that was exactly what i needed.

@J4James maple.mws

@J4James just compare these to answers ! in new code which i upload,compare ans1 and ans2 ! u can see easily maple has found these 4 unknowns ! just see exactly and compare !

Download maple.mws

@J4James it is exact soultion and u use these boundary conditions to determine those Cs 
for solving using numeric process, u should use dsolve(Eq1,numeric) .
be sure this is exact solution.

you should note that answers of the form _C1+_C2*y+_C3*exp(y)+_C4*exp(-y) are also exact soultions, which your first answer dsolve gives that, but boundaries are unknown and should be solved, u use Bcs to make maple find thes unknown c1 and c2 and ... pramateres , but this answer is also exact solution.

numeric soulitons are those which use numeric methods to solve the equation.

if u compare first answer of (dsolve) and second (dsolve,bcs) u can see maple has found those unknown parametes.
good luck!

please do not put picture of your code , i do not think poeple like to write your code again from the picture.thnx

@Kitonum thnx,i saw this answer now, but i think it is exactly what i needed,tnx.

@Carl Love could you please explain more about isprime ? or can i find that in any book ? why u said it takes years of study to understand isprime !? it uses special math ? or what ?

@fernandonobrega 
i will think and study about this, and i hope i can do sth, and hope maple's expert users also help. good luck.

@fernandonobrega please write down the Schrödinger's equation in one variable with a potential V(x) .
i really do not understand the question ! 
i just give an example for solving ode from maple help page :

sys_ode := diff(y(t),t) = x(t),  diff(x(t),t) = -x(t);
dsolve([sys_ode]);
ics := x(0)=1, y(1)=0;
dsolve([sys_ode, ics]);

also if your differential equation is so complicated,u can solve it by dsolve(... , numeric ) option,
please write exactly your differential equation or system of differential equations so that we can solve it.

@Carl Love actually i do not know where is the problem, the problem is continued from our last discussion when we want to seprate the matrix to another matrix multiply in coefficient vector,for example 
eqns:=k.vars
after produncing k , k.a does not equal A since there is some little terms which i think is round off error,
actually when i chande number of digits these errors also change , for example in my own case :

Digits:= 10:
(K.vars - eqns)[1]= -.2e2*a[8]*a[6]+.2e2*a[6]*a[7]+.9e2*a[5]*a[8]

Digits:= 20:
(K.vars - eqns)[1]= .1e-8*a[8]*a[7]-.4e-8*a[8]*a[6]+.2e-8*a[8]^2

Digits:=50:
(K.vars - eqns)[1]=-.1e-38*a[8]*a[7]-.2e-38*a[8]*a[6]

as u can see, when i change digits,the error order differs,now can u tell me what is the problem ?

here is the code itself maple.mws

@toandhsp do u know how to solve it by hand ? if u know this,i think it is too easy to write the code in maple.

@Carl Love you are perfect. i am really thankful since it was a very major problem for me. really thank u.

@Carl Love you are perfect. i am really thankful since it was a very major problem for me. really thank u.