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Your system of equations is underdetermined, so Sage is doing its job by not returning any solution. If you
1) use eq1 and eq4 to eliminate C and D
2) add and subtract the remaining equations
3) rearrange by factoring
you'll see that the remaining two equations are algebraic inverses of each other, i.e., the same equation. You can't get a solution without additional constraints on the functions.
