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The Wronskian of a differential equation of the form is:

where and are solutions of the said equation.

If the Wronskian is nonzero, it means and make up a fundamental set of solutions for the equation.

Relation to Linear Algebra

Recall from linear algebra that, if the determinant of a matrix is nonzero, it means that the two columns of the matrix are linearly independent of each other. Thus, a nonzero Wronskian shows that the solutions and are linearly independent, or make up a fundamental set of solutions.

Abel's Theorem

An alternate expression for the Wronskian (found by algebraic manipulation and similar processes):