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}]].
  • If the functions are linearly dependent, the Wronskian vanishes everywhere.

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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Introduced in 2008
(7.0)