Built-in Mathematica Symbol

Wronskian

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

MORE INFORMATION

The Wronskian determinant is defined as Det[Table[D[y_i, {x, j}], {i, m}, {j, 0, m-1}]].

Linear independence of the functions y₁, y₂, ... is equivalent to the vanishing of the Wronskian.

EXAMPLES

CLOSE ALL

Basic Examples (3)

These functions are linearly independent:

These functions are dependent:

The Wronskian for a linear equation:

In[1]:=

Out[1]=

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

Scope (9)

Properties & Relations (5)

Neat Examples (1)