When Can't You Use the Wronskian Rule?

  • Context: Undergrad 
  • Thread starter Thread starter Thiendrah
  • Start date Start date
  • Tags Tags
    Wronskian
Click For Summary

Discussion Overview

The discussion revolves around the conditions under which the Wronskian can be used to determine the linear independence or dependence of functions. It explores the requirements related to differentiability and the context of the functions involved.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant questions if there are exceptions to using the Wronskian rule for assessing linear independence of functions.
  • Another participant states that the Wronskian cannot be used if the functions are not differentiable.
  • A different participant adds that the functions must all be solutions to the same linear differential equation for the Wronskian to be applicable.
  • It is noted that for the Wronskian to determine linear independence, functions must be differentiable to the appropriate degree (twice for two functions, thrice for three functions, etc.).
  • One participant elaborates that having (n-1) differentials is sufficient to find the Wronskian of n functions, implying a relationship between the number of differentials and the number of functions.
  • A later reply acknowledges a correction made in the discussion.

Areas of Agreement / Disagreement

Participants express multiple views on the conditions for using the Wronskian, indicating that the discussion remains unresolved regarding the full scope of its applicability.

Contextual Notes

There are limitations regarding the assumptions about differentiability and the specific types of functions being considered, which may affect the applicability of the Wronskian.

Thiendrah
Messages
12
Reaction score
0
Is there any exception where I can't use wronskian rule to see if given functions are linearly independent or dependent?

Thanks...
 
Physics news on Phys.org
You can't use the Wronskian if the functions are not differentiable! :biggrin:
 
Indeed, if the functions in question are not all solutions to the same linear differential equation, then the Wronskian does not help.

So, to use the Wronskian to determine whether two functions are linearly independent they must be twice differrentiable, for three functions, thrice differentiable, etc.
 
HallsofIvy said:
So, to use the Wronskian to determine whether two functions are linearly independent they must be twice differrentiable, for three functions, thrice differentiable, etc.

In order to find the wronskian of n functions, it is enough that they have (n-1) differentials because you will then have the same number of equations as the functions. Sorry for being late to the party!
 
Yes, thanks for the correction.
 

Similar threads

Undergrad Determining linear indepedence/dependence of a set of functions
  • · Replies 11 ·
Replies
11
Views
4K
Undergrad Difference between Wronskian and other methods
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Need help interpreting the Wronskian
  • · Replies 1 ·
Replies
1
Views
2K
Graduate What is the connection between the Wronskian and linear independence?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Linearly independence using Wronskian?
  • · Replies 3 ·
Replies
3
Views
2K
Linearly independent functions with identically zero Wronskian
  • · Replies 1 ·
Replies
1
Views
2K
Understanding Wronskian of solutions to homoeneous 2nd order linear DE
  • · Replies 2 ·
Replies
2
Views
2K
Use Wronskian method in solving the given second order differential equation
  • · Replies 7 ·
Replies
7
Views
2K
MHB Compute the Wronskian & Simplify
  • · Replies 6 ·
Replies
6
Views
2K
MHB Use Wronskian to show only 2 indepndent solutions of 2nd order ODE
  • · Replies 4 ·
Replies
4
Views
2K