then u should be assumed as
p
up = xr (A0 sin(αx) + B0 cos(βx)), r = 0, 1, 2, . . . (1.50)
For other forms of g(x) such as tan x and sec x, we usually use the variation
of parameters method that will not be reviewed in this text. Notice that r
is the smallest nonnegative integer that will guarantee no term in up (x) is a
solution of the corresponding homogeneous equation. The values of r are 0, 1
and 2.