# Variation of Parameters help!

Hey all,

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!!

djeitnstine
Gold Member
First of all $$e^{ix}$$ will simplify to sin and cos in each case to make life easier. And you should show us what you have done so far that we may help you. My way of doing it may be slightly different from yours.

Ok,
well simplifying I get these 4 expressions::

C1' cos(x) + C2' sin(x) + C3' xcos(x) + C4' xsin(x) = 0

-C1' sin(x) + C2' cos(x) + C3' xcos(x) - C4' xsin(x) = 0

-C1' cos(x) - C2' sin(x) - C3' xcos(x) - C4' xsin(x) = tan(x)

Now I need to solve this system, and integrate for the constants...

HallsofIvy