# Homework Help: Differential Equations Help

1. Dec 31, 2009

### specwarop

Gday,
Just having a problem doing the initial rearrangement, before I integrate it, of the following differential equation to get the y's and x's on the same side:

(x2+1)y' = xy

Can anyone help me out with this? Ive been trying all day to get both x and y on either side but I cant manage. Is there a trick to it?
Any help appreciated!

Thanks
Matthew

2. Dec 31, 2009

### Hepth

just divide?
x/(x^2+1) = y'/y

3. Dec 31, 2009

### specwarop

Yeh but then on the right side you have (dy/dx)/y
How would you then get the dx over to the left side?

Regards

4. Dec 31, 2009

### Hepth

multiply

$$\frac{x}{\left(x^2+1\right)} = \frac{1}{y} \frac{dy}{dx}$$
$$\frac{x dx}{\left(x^2+1\right)} = \frac{1}{y} dy$$

5. Dec 31, 2009

### specwarop

Okay sweet, thanks for that.
Next dumb question, how do you integrate the left side when dx is up the top like that?

6. Dec 31, 2009

### Hepth

there is no "up top", its all the same, its just a simple multiplication, nothing new or crazy.
$$\frac{x}{x^2+1} dx$$

and try u=x^2+1

7. Dec 31, 2009

### specwarop

Thanks man for your help! Ill have a look at it again tomorrow!
For now, its new years eve time!!! Have fun!