2

Given three functions: $$y_1=x+1 ,y_2=x^3 , y_3=e^x$$ The Wronskian of these three functions at $x_0=0$ is $0$. However the Wronskian at $x_0=1$ is $e$.

Examining the domain $[-2,2]$ the Wronskian is both zero and non-zero over the same domain. How is this possible?

Maryam
  • 1,889
Yisroel Green
  • 31
  • Why should it not be possible? If the Wronskian is identically zero then the functions are linearly independent, but the converse does not necessarily hold. – Martin R Jun 16 '20 at 09:15
  • You are probably thinking of a statement about the Wronskian of solutions of a linear differential equation. If the leading coefficient (i.e. the coefficient of $y^{(n)}$) is nowhere zero then the Wronskian is either identically zero or never zero. That condition is not fulfilled in your case. – Martin R Jun 16 '20 at 09:17

0 Answers0