In my previous post “Solving y’ + a(x) y = b(x), Part 1“, it was revealed that every solution of
is the sum of a particular solution, , with , a solution of the homogeneous equation .
This structure suggests that (1) can be solved in two steps: solve first to get , then change the constant in it to a function and solve for after submitting the variation into (1).
There is an alternative:
From , we obtain
subsequently for yields