WOLFRAM LANGUAGE TUTORIAL
Inhomogeneous Linear Second-Order Equations
If the given second-order ODE is inhomogeneous, DSolve applies the method of variation of parameters to return a solution for the problem.
This solves an inhomogeneous linear second-order ODE. The solution is composed of two parts: the first part is the general solution to the homogeneous equation, and the second part is a particular solution to the inhomogeneous equation.
This solves the homogeneous equation, which is an Euler equation.
Different particular solutions can be obtained by varying the constants C
in the solution.