- #36

- 27,310

- 18,740

Define "disjoint" in this context.Mark44 said:With regard to ##y'' + 9y = \frac 1 2 \cos(3x)##:Sure, this is a particular solution, one that can be decomposed into ##\frac x {12}\sin(3x)## and ##\frac 1{12}\sin(3x)##. The former is a solution to the nonhomogeneous DE above, and the latter is a solution of the homogeneous equation.

My whole argument here is why go out of one's way to devise a particular solution that isn't disjoint from the homogeneous problem's solution set?