Question: A Strange Problem - Nr. 1

Dear MaplePrime users,  I have got a very strange problem ( for me surely)  I am not a mathematician , and not a good Maple user :(((  When you can help me in solving this problem with Maple, you  are very appreciated. Thanx.

Problem:

a, b, c, e,   are constants

X, Y, Z, M, N, R  are time dependent  variables,

X(t)=  Xo- M(t);

Y(t)= Yo - R(t) ;

N(t)= M(t) + R(t);

Z(t)= Zo - M(t) - R(t) ;

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

E= a / c

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)

 Question  1

By eliminationg time domain divinding ( dX / d Y),  What is  E = in terms of X and Y for 

a)  for  Xo  is not eqaul to Yo ( initial X, and Y)

b)  for  Xo = Yo

Question 2:

What will be  time dependent solution of  X and Y  separately ?

Question 3:

if I give a set of time vs X(t)  Y(t) , how can I solve these equations numerically and simulate for the constants ?

Question 4:

How can I plot all above problems ?

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Thank You Very Much for dealers.

Greet

Ironmoon