# Thread: seperable equations

1. ## seperable equations

find the soultion of the differntial equation that satisfies the given initial condition.
xy' + y =y^2, Y(1)= -1

2. Originally Posted by twilightstr
find the soultion of the differntial equation that satisfies the given initial condition.
xy' + y =y^2, Y(1)= -1
Hi

Separating the variables

$\displaystyle \frac{y'}{y(y-1)} = \frac{1}{x}$

$\displaystyle \frac{y'}{y-1} - \frac{y'}{y-1} = \frac{1}{x}$

$\displaystyle \ln|y-1| - \ln|y| = \ln x + C$

Can you go on ?

3. You have a typo. It should be...
$\displaystyle x{dy\over dx}=y^2-y=y(y-1)$
so
$\displaystyle \int {dy\over y(y-1)}=\int {dx\over x}$
then by algebra we have
$\displaystyle \int \biggl({-1\over y}+{1\over y-1}\biggr)dy=\int {dx\over x}$
Now you can integrate and get the correct answer.

4. Originally Posted by matheagle
You have a typo. It should be...
$\displaystyle x{dy\over dx}=y^2-y=y(y-1)$
so
$\displaystyle \int {dy\over y(y-1)}=\int {dx\over x}$
then by algebra we have
$\displaystyle \int \biggl({-1\over y}+{1\over y-1}\biggr)dy=\int {dx\over x}$
Now you can integrate and get the correct answer.
It would help if you quote the post you are responding to, that way it is easier to follow the development of the thread (especially when there is more that one conversation taking place in the same thread).

The quote button is one of the buttons at the bottom right of every post.

CB

5. Originally Posted by CaptainBlack
It would help if you quote the post you are responding to, that way it is easier to follow the development of the thread (especially when there is more that one conversation taking place in the same thread).

The quote button is one of the buttons at the bottom right of every post.

CB

The one right above mine, the only one with a solution here.

6. Originally Posted by matheagle
The one right above mine, the only one with a solution here.
While what you are replying to may have been the last post in the thread when you hit the reply button but that does not mean that it will be the previous post when you hit the submit button. Often someone else will have already been composing a reply, or just have typed faster and got in first.

Also quoting records the content of posts, so a poster cannot remove evidence of asking for help they should not have asked for.

Again, if you comment on a typo, quoting leaves your post still making sense after the typo is corrected.

CB