Although the method variation of parameters can always provide a particular solution to the nonhomogeneous equation, it may not be the simplest way to do so in specific cases.
Find a particular solution of
Let . Then (8.25) becomes
which is a 1st order equation that can be solved using Theorem 8.1 or by inspection. This gives
Using Theorem 8.1, we have, with ,
Even though the integral cannot be evaluated in terms of elementary functions, we can consider the problem solved. The general solution is