You have a differential:
a*f''' + b*f'' + c*f' + d*f + e*f^2 + k*f^3 = 0
Find the f''' .... f^3 in your sequence. Then treat the problem with six different sequences, each scaled by the coefficient. It becomes a simple linear equation in N dimensions and N different sequences. If the sequence numbers overlap, then separate them and adjust the coefficients.
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