Hi!

How do I determine the particular integral for second order differential equations with mixed f(x)s? Like, it's neither strictly polynomial, trigonometry or exponential.

Example of questions,

(i) $\displaystyle y'' - 4y' + 5y = (16x + 4)e^{3x}$

(ii) $\displaystyle y'' + 3y' = (10x + 6)sin x$

(iii) $\displaystyle y'' - 2y' + 4y = 541e^{2x}cos5x$

Thank you! (: