Generalized Buchdahl equations as Lie-Hamilton systems from the 'book' and oscillator algebras: Quantum deformations and their general solution

Rutwig Campoamor-Stursberg, Eduardo Fernandez-Saiz, Francisco J. Herranz

We revisit the nonlinear second-order differential equations $$\ddot{x}(t)=a(x)\dot{x}(t{)}^2+b(t)\dot{x}(t)$$ where $a(x)$ and $b(t)$ are arbitrary functions on their argument f…