372 CHAPTER 9 • z-TRANSFORMS AND APPLICATIONS
4. Solve the homogeneous difference equations.(a) y[2 + n) - 8y[l + n] + 15y(n] = 0 with y[O] = 2, y[l] = 4
(b) y[2 + n) -8y[l + n] + 16y(n] = 0 with y(OJ = 1, y[l] = 3
(c) y[2 + n] - 8y[l + n] + l 7y(n] = 0 with y[O] = 2, y(l] = 4.- (a) Fibonacci numbers. Solve y{n + 2] - y [n + l] - y{n] = 0 with y(OJ = 0,
y[l] = l.
(b) Lucas numbers. Solve y[n + 2] - y [n + 1] - y[n] = 0 with y[O] = 2,
y[l] = l.
- Solve the nonhomogeneous difference equations.
(a) y[2 + n] -6y[l + n] + 8y[n) = 3" with y[OJ = 1, y[l ) = 3.
(b) y[2 + n] - 6y[l + n] + 9y[n) = 2n with y(O) = 2, y[l] = l.
(c) y[2 + n) - 6y[l + n] + lOy{n] = 2•+1 with y[O] = 1, y[l] = 4.- Solve the nonhomogeneous difference equations.
(a) y[2 + n] -8y(l + n] + 15y[n] = 4" with y(O] = 1, y(l) = 4.
(b) y(2 + n] -8y[l + n] + 16y[n] = 5" with y(O] = 2, y[l ] = 1.
(c) y[2 + n] - 8y[l + n ] + 17y[n] = 2 * 3" wit h y[OJ = 0, y[l] = - 1.8. (a) Solve y[n + 2] - h[n + 1] + h(n) = 0 with y[OJ = 1 and y(l] = 3.
(b) Solve y[n + 2) - h!n + l] + h[n] = (fl" with y[O) = 0 a nd y(l] = 1.
9. (a) Solve y[n + 2) - y [n + l] + h(n) = 0 with y(OJ = 1 and y[l] = l.(b) Solve y[n + 2] -y[n + 1] + iy[n] = (~t with y[O) = 0 and y[l ] = l.
- (a) Solve y[n + 2] - ~y[n + l] + y[n] = 0 with y[OJ = 0 and y[l ) = 6.
(b) Solve y[n + 2] - ~y[n + l ] + y[n] = (i" + (-i)") with y[O) = 0 and
y[l] = 1.
- (a) Solve y[n + 2) - h ln + l ] + y[n] = 0 with y[O] = 0 and y[l ] = 6.
(b) Solve y[n + 2] - hfn + 1] + y[n] = (i" + (-i)") with y(O] = 0 and
y[l ] = 1.1 2. (a) Solve y [n + 2] + y[n + l] + y[n] = 0 with y[OJ = 2 and y[l) = - 1.
(b) Solv,e y [n + 2] + y [n + l ] + y[n] = 0 with y[O] = 0 and y[l) = .J3.
13. (a) Solve y(n + 2] - y [n + l ] + y[n] = 0 with y[O] = 2 and y[l] = 1.
(b) Solve y[n + 2] - y [n + l ] + y(n) = 0 with y[OJ = 0 and y[l] = v'3.
- (a) Solve y[n) - .J3y[n - l] + y[n - 2] = 0 with y[O] = 2 and y[l) = v'3.