is Wronskian sign arbitrary?


by 1MileCrash
Tags: arbitrary, sign, wronskian
1MileCrash
1MileCrash is online now
#1
Mar20-13, 06:38 PM
1MileCrash's Avatar
P: 1,227
On my DE test, I was asked to determine if two solutions to a DE are fundamental solutions.

So I confirmed they were both solutions, and took the Wronskian, which was nonzero.

I got points marked off, and he put a minus sign in front of my wronskian result.

Isn't the sign of the Wronskian determined by what function I call y1 and what function I call y2 and is thus completely arbitrary?
Phys.Org News Partner Mathematics news on Phys.org
Math modeling handbook now available
Hyperbolic homogeneous polynomials, oh my!
Researchers help Boston Marathon organizers plan for 2014 race
fzero
fzero is offline
#2
Mar20-13, 10:36 PM
Sci Advisor
HW Helper
PF Gold
P: 2,606
Yes the sign on the Wronskian is determined by the ordering that you assign to the functions. It's a weak excuse, but the grader was probably just comparing your answer with their solution sheet and saw the sign difference and didn't think about why they were different.
1MileCrash
1MileCrash is online now
#3
Mar25-13, 09:38 AM
1MileCrash's Avatar
P: 1,227
Well, I looked at the test and on the paper the functions were called y1 and y2 already, and in my work I did write W[y1,y2] = my wronskian.

So I guess I can understand. I don't think I'll argue this one. I noticed that the wronskian order is arbitrary early off and have just been taking the easier derivative first.


Register to reply

Related Discussions
The Wronskian and the Derivative of the Wronskian Calculus & Beyond Homework 2
I have a Wronskian Question?If the Wronskian W of f and g is t^2*e^t Differential Equations 3
Can Wronskian be used for all? Differential Equations 4
Wronskian Calculus & Beyond Homework 2
Wronskian Calculus & Beyond Homework 7