Question: how to solve this for z in terms of u, x, y

genDE := Diff(g(t),t)^2 - 1 - x*(g(t))^2 - (y-x^2)/12*(g(t))^4 = 0;gensol := dsolve(genDE,g(t));genfun := rhs(gensol[1]);

from above, i got generating function and then continue to derive got the following error

u = ln(-sqrt((-z^2+y)*(-3*z+sqrt(12*z^2-3*y)))*z^2/(sqrt(-z^3*(-3+2*sqrt(3)*csgn(z)))*(-z^2+y)))/x;

tau := subs(u=z,solve(q,z));

it said solution may have lost

if this can not be direct to be solved, any indirect skill to solve it

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