The following functions are solutions to a real constant coefficient homogeneous scalar ordinary differential equation.
(i) Determine the least possible order of the differential equation, and
(ii) Write down an appropriate differential equation.
(a) e-x sin
(b) 3x
(c) xsin x
(d) 1 + xe-x cos2x
(e) sinx + cos2x, sinx + x2 cos x