Solving a coupled system of linear ODEs one second order, the other first order

Question

i want to find Aerodynamic center (y,z) and its moment(M ac) for vehicle , so i searched a lot , and i found these information .

Aerodynamic center position doesn't change wrt angle , drag ,lift forces , pitch moment acts at

i 've done cfd simulations for various angle to get drag ,lift ,moment values ,and i ve made curve fitting for them

so i ve y,z,M ac unknowns while N,A,Mo are known for discrete data

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so i think here i 've coupled system first and second order ,

so how can i solve them ?

if i took more derivatives will it yield to better solution ?

can i apply least square optimization as multi objective function ? and how

i actually tried something which wast right , that i solved system using cramer rule rule , i think that made linearization so i didn't get good result ,am i right ?

i came across into similar question but i cant relate solution to my problem

Solving a coupled system of linear ODEs (one second order, the other first order)

i think we cant solve 2 differential equations when one derived from another so i find another equation . enter image description here

i think i ve under determined differential equation , i don't know if least square optimization can solve it

update 2 , i dont think i ve uder determined system , because with eq 2 , 5 i ve two unknowns y , z with two equations