Question: 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,

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

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