Systematic construction of the ODE system of a circuit containing opamps
The usual small signal approximation used for an op amp operating with negative feedback and in its linear region is that both inputs are always at the same potential, and that the inputs draw no current, i.e. have infinite impedance.  But why are you trying to set up systems of differential equations involving op amps in the first place? Constructing and solving systems of differential equations for more than a few circuit elements is a nightmare.  If all you care about is the small signal behavior of the circuit involving the R,L,Cs and opamps, why not just analyze it directly in the Laplace domain, using the s domain impedances for resistances and capacitances \$\frac{1}{sC}, sL\$?

If you are interested in the large signal behavior of the circuit, then indeed the only way to analyze it is through a system of differential equations.  However, you will then have to use a large signal model of the op amp in question, and no general "algorithm" exists.