Solution to $y'' - 2y = 2\tan^3x$ I'm struggling with this nonhomogeneous second order differential equation
$$y'' - 2y = 2\tan^3x$$
I assumed that the form of the solution would be $A\tan^3x$ where A was some constant, but this results in a mess when solving. The back of the book reports that the solution is simply $y(x) = \tan x$.
Can someone explain why they chose the form $A\tan x$ instead of $A\tan^3x$?
Thanks in advance.

Have you learned variation of parameters? This is a method, rather than lucky guessing :)
http://en.wikipedia.org/wiki/Variation_of_parameters
