Question

@ myininaya
where does the x+c come from in ln|y+1|=x+C
p.s this was in reference to the question "if dy/dx = 1+y, and when x=0, y=2, show that y = 3e^x -1 " you had answered before

Answer 1

I hope I'm not stepping on any toes here by submitting an answer, but in this separable differential equation, you have to integrate the dx term as well. When you integrate the dx, you get an x. You'll end up with a constant term C because you have an indefinite integral.

Answer 2

jabberwock if you want to see what i did you can come here
i think she/he is having a problem with it
http://openstudy.com/groups/mathematics#/groups/mathematics/updates/4e1d1f2f0b8b4841c1a9a219
maybe you can give something helpful to the person
because i guess im not explaining it well

Answer 3

Nah, that looks better than how I would have explained it. Unless there's a specific question, I don't think I could do any better.

Answer 4

LOL @ JABBERWOCK AND MYININAYA
thank you math genuises!

Answer 5

Lol

Answer 6

np

Answer 7

@ jabberwock, y+1=e^x*(3) how did e^{ln3} become (3)? and what happened to the absolute value brackets around y+1

Answer 8

Raising e to a power and taking a natural log are inverse operations. This means that when you do both, they kind of cancel each other out, and you're left with whatever is on the inside.
The absolute value is gone because e to any power is going to be positive. To verify, think about the graph of e^x. It is asymptotic to the line y=0.

Answer 9

i don't get it =[

Answer 10

myininaya, want to take a stab at it?

Answer 11

ln(e^x)=x for all real x
e^(lnx)=x for x>0

Answer 12

wow i don't remember learning that

Answer 13

what about when i did e^(x+C)=e^x*e^C
or was it something else i can't remember exactly but it was something like that

Answer 14

oh i get that part because that is just like x^ab = x^a +x^b

Answer 15

3+a-a = 3
3-a+a = 3

3a/a = 3
(3/a)(a) = 3

\[\sqrt{3^2}=3\]\[(\sqrt{3})^2=3\]
\[\ln(e^3)=3\]\[e^{\ln3}=3\]

All these operations undo each other. In each case, you start with 3, do something to it, undo it, and get back to 3.

Answer 16

OHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

Answer 17

wow thank you so much, i don't think i had learnt that in the log rules. do you know where about in the topic it occurs or maybe i'm just a nutcase and skipped it completely

Answer 18

x^(ab) does not equal x^a +x^b

Answer 19

It's not explicitly taught a lot of times. It sometimes comes out in problem sets though.

Answer 20

the inverse thing?

Answer 21

Yeah

Answer 22

so what does x^(ab) equal to?
lol @jabberwork

Answer 23

Yeah

Answer 24

\[(x^a)^b\]

Answer 25

oh i see, lol i totally fail in math!

Answer 26

lol

Answer 27

thanks guys, i won't harass you no further!
see you

Answer 28

You're fine. Take care.