Separating these equations

**Open that Hampster!** · November 25th 2009, 02:49 PM

1) $(x^2+30)y' = xy$

If I separated it like this:

$\frac{y'}{y} = \frac{x}{x^2+30}$

...can I integrate anyway and get lnY = something?

2) $y' = 38y^2sin(x)$

This is the same above. Getting the y and x variables, but since there's not dx can I then Integrate anyway?

3) $\frac{du}{dt} = 1+u+t+tu$

This one I'm just not sure how to separate.

Any help on these is appreciated. I know they're simple, but well, so am I.

**Danny** · November 25th 2009, 03:29 PM

Originally Posted by Open that Hampster!

1) $(x^2+30)y' = xy$

If I separated it like this:

$\frac{y'}{y} = \frac{x}{x^2+30}$

...can I integrate anyway and get lnY = something?

2) $y' = 38y^2sin(x)$

This is the same above. Getting the y and x variables, but since there's not dx can I then Integrate anyway?

3) $\frac{du}{dt} = 1+u+t+tu$

This one I'm just not sure how to separate.

Any help on these is appreciated. I know they're simple, but well, so am I.

Factor $1+u+t+tu = (u+1)(t+1)$

**galactus** · November 25th 2009, 03:31 PM

You separated fine.

Then integrate and get:

$\int\frac{1}{y}dy=\int\frac{x}{x^{2}+30}dx$

$ln(y)=\frac{1}{2}ln(x^{2}+30)+C$

e to both sides isolates y and gives us a constant $C_{1}$

$y=C_{1}\sqrt{x^{2}+30}$

**Open that Hampster!** · November 26th 2009, 11:38 AM

Thanks for the help. Just two more quick questions:

For the second one:

$y' = 38y^2sin(x)$

$\int y^{-2}dy = \int 38sin(x)$

$-\frac{1}{y} = -38cos(x) + C$

$y = \frac{1}{38cos(x)+C}$

Is this wrong? Is there more than one solution?

And then for the third one, I'm solving for u, so:

$\int (u+1)du = \int (t+1)dt$
$\frac{u^2}{2}+u = \frac{t^2}{2}+t+C$

Not sure where to go to isolate it from here to isolate u.

Happy Thanksgiving everyone.

**HallsofIvy** · November 26th 2009, 05:39 PM

Originally Posted by Open that Hampster!

1) $(x^2+30)y' = xy$

If I separated it like this:

$\frac{y'}{y} = \frac{x}{x^2+30}$

...can I integrate anyway and get lnY = something?

I don't know what you mean by "integrate anyway". Yes, of course, you can integrate $\frac{dy}{y}= \frac{ xdx}{x^2+ 30}$ .

2) $y' = 38y^2sin(x)$

This is the same above. Getting the y and x variables, but since there's not dx can I then Integrate anyway?

Oh, I see. There is a "dx"! y'= dy/dx and you can separate them: $y^{-2}dy= 38 sin(x)dx$ .

3) $\frac{du}{dt} = 1+u+t+tu$

This one I'm just not sure how to separate.

Any help on these is appreciated. I know they're simple, but well, so am I.

Danny told you how to do the last one.

**Open that Hampster!** · November 27th 2009, 06:20 AM

Originally Posted by HallsofIvy

I don't know what you mean by "integrate anyway". Yes, of course, you can integrate $\frac{dy}{y}= \frac{ xdx}{x^2+ 30}$ .

Oh, I see. There is a "dx"! y'= dy/dx and you can separate them: $y^{-2}dy= 38 sin(x)dx$ .

Danny told you how to do the last one.

My post right above yours is my progress after the above two posters.

**dedust** · November 27th 2009, 07:38 AM

Originally Posted by Danny

Factor $1+u+t+tu = (u+1)(t+1)$

using this, we get

$\frac{du}{(u+1)} = (t+1)dt<br />$

integrate it and we're done.

Thread: Separating these equations

LinkBack

Thread Tools

Display

Separating these equations

Similar Math Help Forum Discussions

Separating system of equations

Differential equations, separating variables!

Separating Variables

separating variables! help!

Separating constants

Search Tags