Solving differential equations with exponential terms and a function constraint

[Ado]

Hi!
I need your help for solving a couple of differential equation:

dX/dt = a - b*X

dY/dt = b*(c*exp(-E) - Y) - d*exp(-E)*Y

X = X0 + f(Y, E)

with X0, a, b, c and d are constants and f, a function of Z and E.

Thank you in advance

 

[BvU]

A bit convoluted, this problem statement is. You have a differential equation for X $$
\dot x = a - bx
$$ and a regular equation, $$ x = x_0 + f(Y, E)$$ with $z$ appearing nowhere. Which is it ?

 

[Ado]

Oh yes, it is a mistake ! it is not Z but Y.

 

[Ado]

Problem solved!
Thanks!