Question

How do you simplify lny+c=x-2ln|2+x| to y=Ce^x [(2+x)^-2] ?

Answer 1

http://www.calcchat.com/book/Calculus-8e/

Chapter 6
Section R
Exercise 21

Answer 2

subtract c from both sides and raise e to the power of both sides, then use a few log identities

Answer 3

so then y= -C+(e^x) - (e^2ln(2+x))?

Answer 4

yes, now use \[a\ln x=\ln x^a\] on the middle term

Answer 5

should be
y= -C+(e^x) - (e^(-2ln|2+x|)

Answer 6

y=c+ e^x-(2+x)^2

Answer 7

negative 2???

Answer 8

should be
y= -C+(e^x) + (e^(-2ln|2+x|)

Answer 9

well it's easier if you pit the -2 in the exponent

Answer 10

put*

Answer 11

oh heck
I'm busy and I gave you wrong info

Answer 12

ohh you just put the negative on top rather than leaving it ~ oh ok
so then y= c+e^x+(2+x)^-2

Answer 13

so then how does that get to be multiplied with both C and e^x?

Answer 14

lny+c=x-2ln|2+x| to y=Ce^x [(2+x)^-2]
y=e^(x-2ln|2+x|-c)
y=e^x * e^{-2ln|2+x|) * e^-c

Answer 15

the terms need to be multiplied, not added :P

Answer 16

sorry gotta get dinner, brb

Answer 17

kay thnx

Answer 18

ok, so do you follow up to
lny+c=x-2ln|2+x| to y=Ce^x [(2+x)^-2]
y=e^(x-2ln|2+x|-c)
y=e^x * e^(-2ln|2+x|) * e^-c
?

Answer 19

in LaTeX\[\ln y+c=x-2\ln|2+x|\\y=e^{x-2\ln|x+2|-c}=e^xe^{-2\ln|x+2|}e^{-c}\]