9.1 • THE Z- TRANSFORM 357(a) Use the z-transform and Thbles 9.1-9.3 to find the solution.
(b) Use residues to find the solution.- Solve the difference equation y[n + 1] - 3y(n ) = 4" with initial condition y(O) = 2.
(a) Use the z-transform and Tables 9.1-9.3 to 6nd the solution.
(b) Use residues to find the solution.- Solve the difference equation y[n + 1] - 3y(n] = 4n with initial condition y(O] = 1.
(a) Use the z..transform and Tables 9.1-9.3 to find the solution.
(b) Use residues to find the solution.- In the Newton law of heating and cooling model y(n + l] = aL + (1 - a)y(n], use
the parameters a = k, L = 100 and initial c-0ndition y(O) = 10.
(a) Use the z..tnwsform and Tables 9.1- 9.3 to find the solution.
(b) Use residues to find the solution.- In the Newton law of heating and cooling model y[n + 1) = aL + (1 - a)y[n], use
the parameters a = to, L = 100 and initial condition y[O) = 200.
(a) Use the z-transform and Tables 9.1- 9.3 to find the solution.
(b) Use residues to 6nd the solution.- In the value of an annuity due model y[n+l] = (l+r)(y[n)+P) use the parameters
r = to• P = 1000.
(a) Use the z-transform and Tables 9.1-9.3 t-0 find the solution.
(b) Use residues to find the solution.
1 9. Consider the system of difference equations x[n + lj - y[nJ = 0 and y [n + 1] + x[nJ
= 0 with the initial conditions x(OJ = 1, and y(OJ = 0.
(a) Use trigonometric identities to verify that the solution is x[nJ = cos(~n) and
y(n] = -sin(~n).
(b) Use z-transforms and constr uct the solution in part (a).- Consider the system of difference equations
..;2 ..;2 ..;2 ..;2
x[n + lj =
2
x [n J -
2
y(nJ, and y[n + 1) =
2
x(nJ +
2
y[nJwith the initial conditions x[OJ = l, and y(OJ = 0.(a) Use trigonometric identities to verify that the solution is x(n] =cos( fn)
and y(nJ = sin(f n).
(b) Use z-transforms and residues to construct the solution in part (a).