I have $$ \begin{eqnarray} x'&=& x^2 - y^2 -1 \\ y'&=& 2y \end{eqnarray} $$ How can I solve such a system? I have tried the substitution $X= x^2 - 1$ but I still get constants in the new system as well as square roots this time. I need some advice on the proper substitution to use so as to solve the system. Thank you very much.
2026-05-04 13:42:53.1777902173
Squares and constants in the dynamical system
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