# Wronskian

### From Conservapedia

The **Wronskian** of a differential equation of the form *y*'' + *p*(*t*)*y*' + *q*(*t*)*y* = 0 is:

where *y*_{1} and *y*_{2} are solutions of the said equation.

If the Wronskian is nonzero, it means *y*_{1} and *y*_{2} 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 *y*_{1} and *y*_{2} 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):