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

I really appreciate if you help me.

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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 $x^n,e^{ct},\sin, \cos$.

EDIT: The following link may be useful https://en.wikipedia.org/wiki/Variation_of_parameters

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