Recall that a set of functions is linearly independent if their Wronskian is not identically 0. Calculate the Wronskian of the set to show that they are linearly independent. Write the differential equation for which they are solutions.

The set is:

$\displaystyle e^{\alpha x}, \ xe^{\alpha x}$ <---- I believe that these are not linearly independent, is that the case?

I can do the wronskian... What does it mean to write the differential equation? I'm not sure how to proceed.