Variation of parameters
General · Mathematics
Study notes
Q: Solve y''+y = sec x by variation of parameters. y₁ = cos x, y₂ = sin x. W = 1. u₁' = -sin x·sec x/1 = -tan x: u₁ = ln|cos x|. u₂' = cos x·sec x = 1: u₂ = x. y_p = ln|cos x|cos x + x sin x. y = Acos x+Bsin x+ln|cos x|cos x+x sin x! (Undetermined coefficients can't do sec x!)