Find the General Solution of the Difference Equation $\mathrm { y } _ { \mathrm { k } } = \mathrm { k } ^ { 2 }$

question 7

Multiple Choice

Find the general solution of the difference equation.
-Given that the signal $\mathrm { y } _ { \mathrm { k } } = \mathrm { k } ^ { 2 }$ is a solution of the given difference equation, find a description of all solutions of the equation. $\mathrm { y } \mathrm { k } + 2 + 6 \mathrm { y } \mathrm { k } + 1 - 7 \mathrm { yk } = 16 \mathrm { k } + 10$ for all $\mathrm { k }$

• A) \(\mathrm { k } ^ { 2 } + \mathrm { c } _ { 1 } + \mathrm { c } _ { 2 } ( - 7 ) ^ { \mathrm { k } }\)
• B) \(\mathrm { k } ^ { 2 } + \mathrm { c } _ { 1 } ( - 1 ) ^ { \mathrm { k } } + \mathrm { c } _ { 2 } ( 7 ) ^ { \mathrm { k } }\)
• C) \(\mathrm { k } ^ { 2 } + \mathrm { c } _ { 1 } + \mathrm { c } _ { 2 } ( - 6 ) ^ { \mathrm { k } }\)
• D) \(c _ { 1 } + c _ { 2 } ( - 7 ) ^ { k }\)

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