- #1
Damascus Road
- 120
- 0
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!
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!