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.
Differential equation
