A(x) is the derivative of B(x), similarly B(x) is the derivative of C(x) and C(x) is the derivative of A(x). Then all three are specific solutions to the general differential equation y - y''' = 0.

The general solution to y - y''' = 0 is y(x) = k1*e^x + k2*e^(-x/2)*cos(sqrt(3)x/2) + k3*e^(-x/2)*sin(sqrt(3)x/2), with parameters k1, k2, k3.

Then it would be possible to construct the explicit formulas for A(x), B(x), and C(x) by finding the appropriate coefficients k1, k2, and k3.