Multivariate parameter optimization in "3-states differential equations" where two of the states have measured data and one state lacks data.

I have three differential equations in the form of:

I have measured data:
I do not have data for $$z$$

The initial parameters are $$a,b,c=3,4,5$$

How do I optimize this parameter only knowing the measured value of 2 states only? Thanks in advance.

If you use save_idxs = 1:2, then saveat will only save the values of [x,y] at each time point, and then the parameter estimation routines will compare against two dimensional data.