The following functions are solutions to a constant coefficient homogeneous scalar ordinary differential equation. (i) Determine the

Question:

The following functions are solutions to a 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) e2x + e-3x
(b) 1 + e-x
(c) xex
(d) ex + 2e2x + 3e3x