E.g.f. A(x) and related functions B(x) and C(x) satisfy:
(1a) A(x) = 1 + Integral B(x)*C(x) dx.
(1b) B(x) = 2 + Integral A(x)*C(x) dx.
(1c) C(x) = 3 + Integral A(x)*B(x) dx.
(2a) B(x)^2 - A(x)^2 = 3.
(2b) C(x)^2 - A(x)^2 = 8.
(2c) C(x)^2 - B(x)^2 = 5.
(3a) A(x) = (B'(x) + C'(x))/(B(x) + C(x)).
(3b) B(x) = (C'(x) + A'(x))/(C(x) + A(x)).
(3c) C(x) = (A'(x) + B'(x))/(A(x) + B(x)).
(4a) A(x) + B(x) = 3 * exp( Integral C(x) dx ).
(4b) A(x) + C(x) = 4 * exp( Integral B(x) dx ).
(4c) B(x) + C(x) = 5 * exp( Integral A(x) dx ).
(5a) A(x) = (-5*exp(Integral A(x) dx) + 4*exp(Integral B(x) dx) + 3*exp(Integral C(x) dx))/2.
(5b) B(x) = (5*exp(Integral A(x) dx) - 4*exp(Integral B(x) dx) + 3*exp(Integral C(x) dx))/2.
(5c) C(x) = (5*exp(Integral A(x) dx) + 4*exp(Integral B(x) dx) - 3*exp(Integral C(x) dx))/2.
(6a) A(x)^m = 1 + Integral m * A(x)^(m-1) * B(x) * C(x) dx.
(6b) B(x)^m = 2^m + Integral m * A(x) * B(x)^(m-1) * C(x) dx.
(6c) C(x)^m = 3^m + Integral m * A(x) * B(x) * C(x)^(m-1) dx.
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