Question

when taking integrating factors i obtained e^(ln|x|) as my factor. why do we only consider this as equal to x and not equal to -x (when x<0) ?

Answer 1

wouldn't it be because the argument of ln cannot be less than or equal to 0? since ln 0 is infinity and the ln of negative is undefined

Answer 2

oh never mind, it works haha i made an error

Answer 3

i didnt multiply the RHS by -1 as well

Answer 4

so it was coming out wrong

Answer 5

i think

Answer 6

yes

Answer 7

im not sure though....since i don't think i understand your question well

Answer 8

basically i had an integrating factor coming out as e^ln|u| for some u(x)

so i thought i should consider the case where u <0 separately, but it doesn't matter as doing this results in our IF = -u which gives us the same equation