Rearranging Differential Equations: Getting X's and Y's on the Same Side

[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? I've been trying all day to get both x and y on either side but I can't manage. Is there a trick to it?
Any help appreciated!

Thanks
Matthew

 

[Hepth]

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

 

[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

 

[Hepth]

multiply

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

 

[specwarop]

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

Thanks for your help!

 

[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

 

[specwarop]

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