# Wronskian of x^2 and x^-2

1. Sep 27, 2007

### kasse

What's the wronskian of x^2 and x^-2?

I've found a basis of solutions to a non-homogeneous 2nd order ODE and want to find a particuler solution using variation of parameters.

2. Sep 27, 2007

### genneth

3. Sep 27, 2007

### kasse

But how do I know which function is y1 and y2?

4. Sep 27, 2007

### genneth

Does it matter? What happens to the determinant of a matrix when you transpose two columns or rows?

5. Sep 27, 2007

### kasse

For instance:

W(e^2x, e^x)= (-e^3x)

and

W(e^x, e^2x)= e^3x

Different wronskians...

6. Sep 27, 2007

### HallsofIvy

Staff Emeritus
Yes, you get different signs. Now is that diffence in sign important in your application?

7. Sep 27, 2007

### kasse

Variation of parameters. I think its important.

8. Sep 27, 2007

### genneth

What you will find is that everywhere the Wronskian is use, there's an accompanying minus sign. So if you switch the two solution about, yes the Wronskian changes sign, but so does that the order that the two solutions appear around the minus sign. Thus, there is no difference in the end.