Changes

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

The '''Wronskian''' of a [[differential equation]] of the form <math>y'' + p(t)y' + q(t)y = 0</math> is:

<math>W[y_1, y_2] =

<math>W[y_1, y_2] =

== Relation to Linear Algebra ==

== 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 <math>y_1</math> and <math>y_2</math> are linearly independent, or make up a fundamental set of solutions.

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 <math>y_1</math> and <math>y_2</math> are linearly independent, or make up a fundamental set of solutions.

== Abel's Theorem ==

== Abel's Theorem ==