Given a 2nd order ODE for y(x) which doesn't depend on x:
Find a reduction of order to a 1st order ODE, and the associated transformation:
Solve the reduced order ODE:
Apply the transformation to find a simpler ODE for the original variable y(x):
Solve the simpler ODE to find the general solution of the original ODE:
Alternatively, the original ODE can be solved in a single step if we use the option solve:
Another example: