Your opinion on a class of ODE problems

[Namir]

For the consecutive reversible reactions:

A <--> B <--> C

The equations are:

d[A]/dt = -k1[A] + k'1[B]

d[B]/dt = k1[A] - (k'1 + k2) [B] + k'2[C]

d{c]/dt = k2[B] - k`2[C]

Where [A], [B], and [C] are the concentrations for chemicals A, B, and C, respectively. The forward reaction rates constants are k1 and k2. The reverse reaction rate constants are k'1 and k'1.

As you can see the ODEs are not complicated. The analytical solutions are complicated. I am trying to find a general method where the analytical solution for the differential equations is way too complicated.