Determine the general solution of the second-order differential equation

The homogeneous equation related to this is an equation of the form with and . This gives us and . So, the general solution of the homogeneous equation is given by

Then we know that and are particular solutions of the homogeneous equation (taking and , respectively). The Wronskian of and is given by

Thus, a particular solution of the non-homogeneous equation is given by (from Theorem 8.9)

This implies

Therefore, the general solution is