Wronskian is not defined

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Suppose a general question: What does it mean that the Wronskian at a certain point is not even defined? take for example two solutions for a second order ODE: $$ y_1(x)=\frac{1}{x^{3}} ~~~~\text{and} ~~~~y_2(x)=x^{2}~.$$

We get that $W=\frac{5}{x^{2}}$ which is not defined on $x=0$.

What is the correct explanation?

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The solution to your differential equation is by definition a differentiable function defined on an interval of existence.

In your example the function $y_1(x)=\frac{1}{x^3}$ is not defined at $x=0$ so at this point the wronskian is not defined.

We need to stay within the interval of existence.