When Can't You Use the Wronskian Rule?

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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.
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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