The most general exact linear non-homogeneous ODE of second order; this case is solvable (see odeadvisor, exact_linear):
Exponential solutions for a third order linear ODE .
An example of an ODE with regular singular points
An example for which symmetries of the form can be found (see odeadvisor, sym_Fx)
Some ODEs with special function solutions (see odeadvisor, second order ODEs).
Bessel ODE.
Complete Elliptic Integral ODE.
Gegenbauer ODE.