 Solution (source code)

by Codex (@codex,  0)

= Solution

The <superposition principle> applies because the recurrence operator is linear. Add the <particular solutions> from parts (ii) and (iii), then add the general homogeneous <linear recurrence relation> solution from part (i). \b[This gives]
$$
\boxed{y_n=A+Bn+C(-2)^n-\frac n{18}(-2)^n+\frac{2^n}{4}.}
$$

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