Consider the difference equation \(y\left[ n \right] - \frac{1}{3}y\left[ {n - 1} \right] = x\left[ n \right]\) and suppose that \(x\left[ n \right] = {\left( {\frac{1}{2}} \right)^n}u\left[ n \right]\). Assuming the condition of initial rest, the solution for y[n], n ≥ 0 is

• A. \(3{\left( {\frac{1}{3}} \right)^n} - 2{\left( {\frac{1}{2}} \right)^n}\)
• B. \(- 2{\left( {\frac{1}{3}} \right)^n} + 3{\left( {\frac{1}{2}} \right)^n}\)
• C. \(\frac{2}{3}{\left( {\frac{1}{3}} \right)^n} + \frac{1}{3}{\left( {\frac{1}{2}} \right)^n}\)
• D. \(\frac{1}{3}{\left( {\frac{1}{3}} \right)^n} + \frac{2}{3}{\left( {\frac{1}{2}} \right)^n}\)