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this is a little confusing, because the "variation of parameters" that I have been taught in class is different then what I find in most texts...

I have y''' + y' = tan(x)

Most textbooks use the wronskian and work from there,

what I was taught to do is set it up as the characteristic eqn, and then factoring it I get solutions

r = 0, -i , + i

(Side question, may I set up my solution as:

y= C1 + C2sin(x) + C3cos(x) + C4 e^ix + C5 e^ - ix ?

or must it be something like...

y= C1 +C2 e^ix + C3 e^ - ix + C4 xe^ix + C5 xe^ - ix ? )

Anyways,

then when we take the derivatives, we end up with a system of equations, where the sum of each term with a derivative of a constant = 0,

and the last expression = tan x

But solving these is difficult...

HELP!!