Question

Solve the initial value equation for x(t): dx/dt = 1-x^2, x(0)=3

Answer 1

I got \[t(x) = \frac{ 1 }{ 2 }\ln \frac{ |x+1| }{ |x-1| }+3\]

After integrating.

Answer 2

Book says the answer is:

\[x(t) = \frac{ 2+e ^{-2t} }{ 2-e ^{-2t} }\]

I don't know how they got there.

Answer 3

How did you integrate?

Answer 4

Apparently wrong, hold on while I redo everything from the integration down.

Answer 5

Err, I got excited for nothing, integration was right, so my partial fractions were:

\[dx = \frac{ 1 }{ -2(x-1) }+\frac{ 1 }{ 2(x-1) }\]

Answer 6

why is your x-1 on top?

Answer 7

Can you confirm the partial fractions above?

Answer 8

I used
dx / (1-x^2)= A / x+1 + b / ( 1-X)

Answer 9

does that help ? B=1/2, A=1/2

Answer 10

The solutions used (1-x) too, but I don't know why I can't use -(x-1)(x+1) and get the same answer.

Answer 11

Every time I try to think on my own, wrong, wrong, wrong.

Answer 12

you certainly can , but then you need to care for the " - ve sign " and use properties of log to rewrite : )

you may be correct, DONT ALWAYS COMPARE your answer with book. If you do need to compare, work backwords to your answer.

Answer 13

Can you arrange it my way and try to work though it with me?

Answer 14

I would say THERE IS NO POINT in writing that -ve sign "your way" , it may complicate matters.

Save time : )

Answer 15

But you understand its frustrating not being able to complete a problem in your own way right?

Answer 16

I dont see reason for frustration, what matters is the approach to solve the problem

Answer 17

did you get
1/2 * [ ln |(1+x)]| +1/2*[ln|(1-x)|]=t+ K

Answer 18

- 1/2 ln(1-x)

Answer 19

put x=3 and t=0

1/2 * [ln(1+3)]+1/2*[ln|(1-3)|]=0+K

Answer 20

I'm going to upload a pic of my sheet, hold on a sec.

Answer 21

Okie

Answer 22

the work is all fine, until the very last step, you DO NOT need that negative sign, you have already taken care of it

Answer 23

ok, so now I'll find c

Answer 24

if you say -ln(a)+ln(b)= ln (b/a), then there is NO NEED to write it as - ln (b/a)

Answer 25

Ya, I get it, I make a lot of dumb errors

Answer 26

before you find C, make sure you correct your mistakes, a mistake of an incorrect sign will give incorrect values of C

Answer 27

So it appears C is 1?

Answer 28

and dont compare your answer with book, you are on right track, just find value of C and leave it as it is.

Answer 29

I hope that helps, am taking off here

Answer 30

Nooooooooo, I need you