Wronskian

Wronskian[{y1, y2, ...}, x]
gives the Wronskian determinant for the functions depending on x.

Wronskian[eqn, y, x]
gives the Wronskian determinant for the basis of the solutions of the linear differential equation eqn with dependent variable y and independent variable x.

Wronskian[eqns, {y1, y2, ...}, x]
gives the Wronskian determinant for the system of linear differential equations eqns.

DetailsDetails

  • The Wronskian determinant is defined as Det[Table[D[yi, {x, j}], {i, m}, {j, 0, m-1}]].
  • Linear independence of the functions is equivalent to the vanishing of the Wronskian.

ExamplesExamplesopen allclose all

Basic Examples (3)Basic Examples (3)

These functions are linearly independent:

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These functions are dependent:

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The Wronskian for a linear equation:

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Except for a constant, the result is the same as for the explicit solution:

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