Find the general solution of the second-order differential equation
If the solution is not valid everywhere, describe the interval on which it is valid.
The general solution of the homogeneous equation
is given by Theorem 8.7 with and . This gives us ; hence, . Thus,
To find a particular solution of assume is a solution. Then,
Then, let . This implies
Hence, which gives us the particular solution
Finally, the general solution is then