# Fit with implicit functions?

Is it possible to make a least squares fit with a function given implicitly, because the equation isn't solveable analyticly? Because I had the coupled ODE,

$$\ddot{x} = \omega^2x + 2\omega\dot{y} - C\,\frac{\dot{x}}{\dot{r}}$$

$$\ddot{y} = \omega^2y - 2\omega\dot{x} - C\,\frac{\dot{y}}{\dot{r}}$$

where $\dot{r} = \sqrt{\dot{x}^2+\dot{y}^2}$, and $\omega$ and C are constants in time.
I can numerically solve this system and make a plot in x-y, but I also have some measurement data, so is there a way to make best fit of the "solution" to the data points? That is vary the 2 constants to make a best fit?
There are also the 4 initial conditions when solving this system of ODE, how will they be involved in this?

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