Let us consider the differential Operator L : 03([0,7r]) > C([ELs-D dened as Ly = y"' with hemo- geneous D Dirichlet boundary conditions at t = 0 and t = 1r. Is this a regular SturmLiouville operator? Using the eigenfunctions of this operator and the fact that any square-integrable function on [I], r] can be expanded in Fourier series (using the eigenfunctions) and this series converges in L2-sense to the corresponding function itself, we are aiming to solve dierential equations of the form Ly = f (ODE) using the technique of Fourier series expansion. (1) Let f : [0,7r] be dened as f(t) = 2. Can one solve the (ODE) with this r.h.s.? If yes, give the solution in terms of Faurier series. (2) Let f : [0,51] be dened as f(t) = t. Can one solve the (ODE) with this r.h.s.? If yes, give the solution in terms of Fourier series. (3) Let f : [0,11'] be dened as f(t) = tan(t). Can one solve the (ODE) with this r.h.s.? If yes, give the solution in terms of Fourier series. (4) Let f : [0, 11'] be dened as f(t) = eos(t). Can one solve the (ODE) with this r.h.s.? If yes, give the solution in terms of Fourier series. (5) Let f : [0, 7r] be dened as t) = sin(5t). Can ene solve the (ODE) with this r.h.s.'? If yes, give the soluticm in terms of Fourier series