Determine the solutions of the difference equations below, supposing that the systems they represent are initially relaxed:

(a) \(y(n)-\frac{1}{\sqrt{2}} y(n-1)+y(n-2)=2^{-n} \sin \left(\frac{\pi}{4} n\right) u(n)\)

(b) \(4 y(n)-2 \sqrt{3} y(n-1)+y(n-2)=\cos \left(\frac{\pi}{6} n\right) u(n)\)

(c) \(y(n)+2 y(n-1)+y(n-2)=2^{n} u(-n)\)

(d) \(y(n)-\frac{5}{6} y(n-1)+y(n-2)=(-1)^{n} u(n)\)

(e) \(y(n)+y(n-3)=(-1)^{n} u(-n)\).