The Liouville ODE has the following symmetries (see dsolve,Lie):

These symmetries can be tested using symtest

Knowing two independent symmetries for a second order ODE almost always leads to its answer, as in the following Liouville ODE:

Implicit and explicit answers for ODEs can be tested using odetest.

DEtools, odeadvisor, dsolve, and ?odeadvisor,<TYPE> where <TYPE> is one of: quadrature, missing, reducible, linear_ODEs, exact_linear, exact_nonlinear, sym_Fx, linear_sym, Bessel, Painleve, Halm, Gegenbauer, Duffing, ellipsoidal, elliptic, erf, Emden, Jacobi, Hermite, Lagerstrom, Laguerre, Liouville, Lienard, Van_der_Pol, Titchmarsh; for other differential orders see odeadvisor,types.