\left( D' \right)^2 + B'' - {B' D''}/{D'}. \end{aligned}$$ The data presented here was described well by the trial function (\[trialfn\]) using the polynomials $$\begin{aligned}
   \label{Bt}B(t) &= \alpha_1 t + \alpha_2 t^2 + \alpha_3 t^3 \\ D(t) &= \omega_1 t + \omega_2 t^2 + \omega_3 t^3, \label{Dt} $$ where the fit parameters $\alpha_i$ and $\omega_i$ are independent of time. In contrast, an RLC circuit with constant parameters is described by the polynomials $B(t) = t \, R/(2L)$ and $D(t) = t \sqrt{1/(LC)^{2} - R^2/(2L)^2}$.

After fitting data with the trial function (\[trialfn\]), the reconstructed differential equation (\[recoveredDE\]) may be used with the appropriate differential equation from above to estimate the time-dependent circuit parameters $C(t)$ and $R(t)$. For the data presented here, this analysis was simplified using the following approximations. For the current data, the approximation $$\begin{aligned}
   \label{Iapprox} 
\left| R C' + R' C \right| \ll 1\end{aligned}$$ simplifies the differential equation (\[Ide\]) to $$\begin{aligned}
I'' + \left( \frac{R}{L} + \frac{C'}{C} \right) I' + \left( \frac{1}{LC} \right) I  \approx 0. \end{aligned}$$ Using this with (\[recoveredDE\]), the circuit parameters may be estimated using $L$, (\[Ut\]–\[Dt\]), and the fit parameters $\alpha_i$ and $\omega_i$ as $$\begin{aligned}
 \label{CtI} 
C(t) &\approx 1/[{L \, W(t)}] \\
R(t) &\approx 