Question

x' - x = sint + cost
How do I solve this?

Answer 1

whats the prime with repect to?

Answer 2

respect*

Answer 3

t?

Answer 4

yes with respect to t

Answer 5

first order linear differential equation => use Lebnitz method

Answer 6

http://www.sosmath.com/diffeq/first/lineareq/lineareq.html

Answer 7

aka Exact equations...I used this and got x(t) = -sint - cost, for the parametric part
But the answer says x(t) = -cost

Answer 8

Not really sure about that!!!

Answer 9

experiments way is how i wold do it...

Answer 10

find an integrateing factor... multiply thru.. intgrate both sides...

Answer 11

sounds like ur way may be easier but we never learned those..

Answer 12

I used an integrating factor, I just know it by a different name, not sure why I'm not getting the right answer

Answer 13

Well, it it's worth trying.

Answer 14

the method I used is the same as Lebnitz

Answer 15

check to make sure your integrateing factor made it thru to both terms and that both terms were integrated

Answer 16

correctly

Answer 17

Solution is attached.

Answer 18

the I.F. = e^(-t)
on multiplying it to the equation you get \[\int\limits_{}^{}e ^{-t}(\sin t - \cos t)dt\]

Answer 19

Ok looks like I made a mistake in the integration, I do -cos t now

Answer 20

But I'm wondering if there is a quicker way to solve this

Answer 21

Thanks a lot robtobey. Seems like I.F. is the quickest way

Answer 22

use e^xCosx = http://answers.yahoo.com/question/index?qid=20080723161756AA9xWm6

Normally I take this as formula

Answer 23

Thanks for that formula, a little to hard to remember but useful nonetheless

Answer 24

well, ... best of luck.

Answer 25

thanks