I am currently taking a class on Fundamentals of Differential Equations. The textbook is of the same name and authored by Nagle, Saff, and Snider.
I don't completely understand the derivation of the variation of parameters method for solving an ODE. Particularly the part where we assume that the particular solution of the ODE is of the form $v_1(t)y_1(t) + v_2(t)y_2(t)$.
What allows this assumption? In my opinion it seems like a huge assumption to make.