When Can't You Use the Wronskian Rule?

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SUMMARY

The Wronskian rule can only be applied to determine the linear independence of functions that are differentiable to the required degree. Specifically, for two functions, they must be twice differentiable; for three functions, thrice differentiable, and so on. Additionally, all functions must be solutions to the same linear differential equation for the Wronskian to be applicable. If these conditions are not met, the Wronskian does not provide valid information regarding linear independence.

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Is there any exception where I can't use wronskian rule to see if given functions are linearly independent or dependent?

Thanks...
 
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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.
 

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