Coupled ODE's with constraints How do we solve a a system of ODE's:
$\frac{dc_i}{dx} = f_i (c_i, x) $
Where $f_i $ can be linear or non-linear. Subject to:
$\sum{\alpha_i c_i} = 0$?
More specifically, this is the system of equations I'm looking at:



The system had better be consistent with the constraint, i.e. (assuming $\alpha_i$ are constants) 
$$\dfrac{d}{dx} \sum_i \alpha_i c_i = \sum_i \alpha_i f_i(c_i, x) = 0$$
If so, just solve the constraint for one of the $c_i$ and substitute in to the differential equations for the other $c_i$'s.
