# How to Solve the Following D.E.?

1. Sep 10, 2006

### Iron Eagle

Hi guys,

I'm stuck trying to separate the following equation, not really sure how so separate it:

Thanks for any inputs!

Last edited: Sep 10, 2006
2. Sep 10, 2006

### arildno

You can't separate it as it stands, so play a bit around by trying to change the independent or dependent variable.

3. Sep 10, 2006

### Iron Eagle

Could you explain how that would work? You're right, it's supposed to be x(y) and when y=1, x=3. But I'm not sure how to put that info to use. TIA.

Last edited: Sep 10, 2006
4. Sep 10, 2006

### arildno

Well, lets for fun's sake make our new dependent variable:
$$u(x)=9-5xy^{2}(x)\to{y(x)=\sqrt{\frac{9-u}{5x}}$$
Now, find an expression for dy/dx and y^3 in terms of x and u.

Substitute all of this into your diff.eq, if you are lucky, you've gotten a separable diff.eq in u and x.
Probably, it won't work with this choice; you can have hours of fun trying out different changes of variable.

5. Sep 10, 2006

### Iron Eagle

Thanks, with your help I was able to figure out the answer. Much appreciated!

6. Sep 11, 2006

### HallsofIvy

Staff Emeritus
Try an integrating factor of the form yn.