Question

Please solve using the general solution method. Do not use Z-Transforms.

3.34. Consider the second-order homogeneous difference equation with initial conditions yl-1] pi and yl-2 P2. The coefficients a and a2 of the difference equation and the initial values p? and p2 are all real-valued, and will be left as parameters. a. Let z1 and 22 be the roots of the characteristic polynomial. On paper, solve the homogeneous difference equation for the three possibilities for the roots: 1. The roots are real and distinct. 2. The roots are a complex conjugate pair. 3. The two roots are real and equal. Find the solution vin] as a function of the roots 21 and z2 as well as the initial values p? and p2.

Answer 1

7ven euatr Havmg equation we hav-e chanacteristeqatton 2

4-B A&B 2. 2 2 122 고1

2-1 2C22-2 212 complex conjugat 2 2 군 2 2-

Similan tee have 2 ろ A -20 2-