Dear Mathematicians ,

May I get any help for the above mentioned problem please ?

Dear Robert Israel,

I am not amthematician and I can not really understand these concepts, I have never used  LSSolve,

may I request you that you solve this numerically for me please, and plot it.

that will be very very graceful

thanks, greets

poor Ironmoon :(((

Dear Israel,

yes  this equation  reduces into what you have shown, now we can take this equation into account and use it for the rest of problem :)

It is for me very  complicated  since I look for different solution

for example

question 1) if b=e=0

how can I solve this equation and how can I find a, c  with the given data set ( I mean how can I simulate it with maple )

question 2)

if b and e are not zero what can be the solution

Thanx for your deal

Dear Robert ISrael,

un the   new defined parameters,  K= b/a = e/c = X / M =  Y/ R

the ratio of time dependent  X(t)/ M/t) and Y(t)/R/t)  are constant, but this is just an information, it may not be used in the solution.

Perhaps it is better  solve this problem stepwise.

1-

X(t)=  Xo- M(t);   >  M/t) = Xo-X(t)

Y(t)= Yo - R(t) ; > R(t)= Yo - Y(t)

N(t)= M(t) + R(t);  > N(T)  = Xo - x(t)  + Yo - Y(t)

Z(t)= Zo - M(t) - R(t) ;   >  Z(t) = Zo - Xo- + X(t) - Yo + Y(t)

new defined parameters,  K= b/a = e/c 

E= a / c

 Let us substitute    X(t), Y(t)  and  M(t) in x ,  N(t) in Y

ODE functions are system ODE  for simultaneous solution

dX/ dt = b.M(t). N(t) - a. X(t). Z(t)

dY/ dt = e. R(t). N(t) - c. Y(t). Z(t)

dX/dY = [ b: M(t): N(t) - a. X(t). Z(t) ]   /   [ e.R(t). N(t) - c.Y(t). Z(t) ]

---------------------------------

is it

 possible to find  E= a / c =  after solvung this new ODE

thank you

Dear Robert Israel,

Y(t)

X(t)   are different functions but effect each other, so should it be two different separate

Y vs. t   and  X vs. t    curves on the same  2 D coordiantes  ?

greets

AA /  Germany

Dear Robert Israel,

thank you sooooo much for your approach, now I try to understand them all. I wish I had been a mathematician and also good at maple :(((((

May I send you experimental real values if you still want to help me?

thanks

AA

Dear Robert Israel,

I am very thankful to all who worked for this problem. I now got :) that the closed forms have no soln.

May I ask another question please ?

If I have a data set of

t                               x(t)                                        y(t)

0                               1                                             1

1                                 0.9                                      0.8
 

2                                0.8                                       0.5

and so on,

how can it be possible to to simulate

 [ dy/dt ]  = m ( a + b* y(t) + c* x(t) + d* x(t)* y(t)+ f *y(t)^2 ) 

 [ dx/dt ] = n  ( a + b*x(t) + c*y(t) + d* x(t)*y(t) + f* x(t)^2 )

both equations simultaneously to detect the values of the coefficients ?

sorry for my foolish questions, but I need them :(

thanks soooooo much

AA / Germany

Dear Alec,

sorry in previous message, so has been son :) anyway, I appled your suggestion and waited more than a hour, nothing came out :(((((  I do not know how long one can wait to understand if maple has a solution.  For coefficients, unfortunately they are physically exiting therefore I can not make them zero...

I have another queation, if you still want to help me.

in this equation, e value should be detected as ratio of  y and x , how can I make numerical solution if dy/dx also exits in the equation ? or how can I  solve system

dy/dt = f( y,x)

dx/dt:f(y,x)

simultaneously :(((  

thank you very much

AA / Germany

Dear Alec,

I applied your suggestion and run maple. It run for 40 min and vitual problem exited, son I had to stop running :((((

thanks for your helps, I hope there will be a solution :)

AA

sorry,  sometimes being fool is the good way of learning  :)

why  f =1 and c = 0,

I try to run maple for the last case

greets

AA

Dear Writers,

thank you all for the suggestions but I am not a mathematician :(   therefore It seems difficult for me to follow you in detail.

Dear Alec, if possible , could you  please send me maple file so that I can wait till the end of solution.

this equation comes from a physical modelling :(

thank you

AA

Dear Robert Isreal,

first of all I appreciate that you spent time for me :) thank you.  This is a really a big problem for me that I was not able to solve :((((  I hope Maple 13 can solve this  :))problem :))))

However I require the complete solution especially for  e value :)

Thanks a lot

AA