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My idea has been written down here, check out

Equivalence_class_of_solvable_Abel_and_Riccati_equation_(2).pdf

[moderator: updated with new approach, as follows, Feb 5, 2024]

Equivalence_rational_transformation_of_Riccati_equation_(7).pdf
We have found new way to find equivalence transformation that yields a rational differential equation to Riccati equation, therefore computing non-Liouvillian first integral will be possible. This method can be implemented by Maple.
ode dsolve differential-equations

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