Geogebra makes it especially easy to numerically simulate differential equations. To write the equations, we use prime notation so
A'= dA/dt
First put in each of your differential equations. For the A<==>B<==>C I am letting k1 , and k3 be the forward rate constants and k2 and k4 be the reverse rate constants. Enter the 3 differential equations with the input bar as here. You will also be prompted to put in the k values as sliders. Range these from 0 to 0.1
A'( t,A,B,C )= - k1*A + k2*B
B'( t,A,B,C )= k1*A - k2*B - k3*B + k4*C
C'( t,A,B,C )= k3*B - k4*C
Next enter the initial conditions. In this case I am starting with 10 μ M of compound A and no amount of B or C. Since Geogebra usually starts its y-scale with integers, you may have to stretch the y-scale until ymax is about 1E-5.
A0=10E-6
B0=0
C0=0
Finally, we put in the numerical solving equation:
NSolveODE[ {A',B',C'},0,{A0,B0,C0},200 ]
The four entries are 1) the differential equations, 2) the starting time, 3) the initial conditions, and 4) the end time.
This Runs really slow on most browsers because of the massive amount of calculation. It is much much faster on your PC, so download the ggb file and run it yourself.

Run your own simulations with DEs that you have origintated.