I would do the Wronskian only to check: Let such that then evaluating in gives and in gives so they are l.i.
As for the second question here's what I would do:
Clearly is satisfied by . The second one is trickier let such that then after some calculations we get now but we take and and we get (this results from taking , substituting in the equation and then multiplying by the whole thing). And with this equations we have a representation of and what I think you're asked is to try and find a second order (linear) dif. eq. such that is the set of solutions of said equation.