Wronskian

The Wronskian is a tool to show that a set of functions are linearly independent. Given the aforementioned set of fundtions and each function posses derivatives the Wronskian () is as follows:

where is the determinant.

If you can prove that the Wronskian of a set of solutions to a differential equation () is not equal to 0 on an interval the set is said to be linearly independent on that interval.

See W2L4 - Higher Order Linear ODEs for more information and examples.