The problem instructions read like so:

Show that the given functions are linearly independent on the interval I and ﬁnd

a second-order linear homogeneous equation having the pair as a fundamental set of

solutions.

I'm able to prove that they are linearly independent easily by simply using the Wronskian Matrix to get

However, I don't know how to find the equation based off of what I'm given.

I know the answer to the question (it's in the book) so I will post it for reference of what I'm looking for.

please show me the method to find this equation based off of the fundamental set given!