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Need help interpreting the Wronskian

  1. Jan 6, 2016 #1
    I'm given bases for a solution space [itex]\left \{ x,xe^x,x^2e^x \right \}[/itex]. Clearly these form a basis (are linearly independent).

    But, unless I've made a mistake, doing the Wronskian on this yields [itex]W(x) = x^3e^x[/itex].

    Isn't this Wronskian equal to zero at x = 0? Isn't that a problem for dependence/independence?

    note: a DE to which this solution space applies has not been provided in the exercise.
  2. jcsd
  3. Jan 6, 2016 #2


    Staff: Mentor

    No. The three functions are linearly independent on any interval that doesn't include 0. I'm assuming that you correctly evaluated the Wronskian.
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