# How to solve this $y'' +y = 2 \sec(3x)$ differential equation?

I am having trouble with differential equations. $$y'' +y = 2 \sec(3x)$$

I really appreciate if you help me.

I assume you know the homogeneous solution $y'' + y = 0$ leads to $y(x) = c_1 \sin x + c_2 \cos x$. The particular solution is probably easiest to solve using variation of parameters. The guess of $\sec (3x)$ or $\tan (3x)$ does not work. Guessing is usually only done with $x^n,e^{ct},\sin, \cos$.