Let the functions f(t) = e^t and g(t) = t defined on R.

(i) Show using the Wronskian that f and g are linearly independent on R.

(ii) Use the Wronskian to determine the two intervals over which these two functions could be the solution of an ODE of the form y^,, +p(t)y^, + q(t)y = 0 and for which Abel's theorem would apply.

(iii) Find the ODE of the form given in (ii) of which f and g are solutions, and verify that this ODE is indeed defined only on the intervals obtained in (ii).