Find the General Solution of the Difference Equation $y _ { k } = 3 k - 5$

Multiple Choice

Find the general solution of the difference equation.
-Given that the signal $y _ { k } = 3 k - 5$ is a solution of the given difference equation, find a description of all solutions of the equation. $y _ { k + 2 } - 6 y _ { k + 1 } + 5 y _ { k } = - 12$ for all $k$

A) $3 \mathrm { k } - 5 + \mathrm { c } _ { 1 } + \mathrm { c } _ { 2 } ( 6 ) ^ { \mathrm { k } }$
B) $3 \mathrm { k } - 5 + \mathrm { c } _ { 1 } ( - 1 ) ^ { \mathrm { k } } + \mathrm { c } _ { 2 } ( - 5 ) ^ { \mathrm { k } }$
C) $\mathrm { c } _ { 1 } + \mathrm { c } _ { 2 } ( 5 ) ^ { \mathrm { k } }$
D) $3 \mathrm { k } - 5 + \mathrm { c } _ { 1 } + \mathrm { c } _ { 2 } ( 5 ) ^ { \mathrm { k } }$