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Thread: Wronskian computation

  1. #1
    Junior Member
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    Wronskian computation

    Given set of functions: 1, x, x^2, x in any interval; compute the Wronskian of this given set of functions and then determine whether the function is linearly dependent or independent. Could someone explain how to go about this? Thanks,

    Jim
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi

    For three functions f_1,\,f_2,\,f_3, the wronskian is W(x)=\left| \begin{array}{ccc}<br />
f_1(x) & f_2(x) & f_3(x)\\<br />
f_1'(x) & f_2'(x) & f_3'(x)\\<br />
f_1''(x) & f_2''(x) & f_3''(x)<br />
\end{array}<br />
\right| and the functions are linearly independent if the wronskian is nonzero.
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