find a particular solution to y"+9y=9sec^2(3t)?

Question

help with this problem please. find a particular solution to y"+9y=9sec^2(3t)

Answer 1

What are we trying to do with this problem?

Answer 2

Use variation of parameters.

The particular solution will have the form

A(x)u1(x) + B(x)u2(x)

where u1(x) and u2(x) are two linearly independent solutions of the homogeneous problem, y'' + 9y = 0. These solutions are cos(3t) and sin(3t).

Formulas for A(x) and B(x) are given on the web page listed below.