Mehdi H. answered 02/23/24
Teaching High Level Math Courses
The two linearly independent solutions to the homogeneous equation y''+y=0 are sin(x) and cos(x). Use Variation of Parameters formulas to find the particular solution.
I think "reduction of order" means use Variation of Parameters. Otherwise, reduction of order (Abel's Theorem) is used for homogeneous equations when we know one solution. In this problem we know both solutions to the homogeneous equation.