``````````````````````````````````````````````````````````````````````````````````` Solve these recurrence relations together with the initial conditions given. Recall that the solu-tion to a second order recurrence relationan = can-1 + C2An-2will be of the formf(n) = a¡r{" + a2r".Where ri, r2 are roots to the characteristic equation of a,andk1 – kor2ri- r2kori – kia2 =ri- r2with ko = ao and k1 = a1. Or if the roots are repeated, it will be of the formf(n) = a¡r" + a2nr".where a1 = ao.Find the solution for an = 8an-1 – 16an-2 for n> 2 and ao = 1, aį =2.1.2.Find the solution for a, = 8an-1 - 16a,-2 for n2 2 and a = 5, a1 = 7. Note: Thisdiffers from the previous problem only by its initial conditions.

(1) Given the recurrence relation is an=8an-1-16an-2, a0=1, a1=2. an=8an-1-16an-2an-8an-1+16an-2=0…

Solve these recurrence relations together with the initial conditions given. Recall that the solu- tion to a second order recurrence relation An = C1 An-1+ C2An-2 will be of the form f(n) = a,r" + a2r". Where r1, r2 are roots to the characteristic equation of a, and ki - kor2 kor - ki a2 = with ko = ao and kį = aj. Or if the roots are repeated, it will be of the form f(n) = a\r" + a2nr". where a = ao. Find the solution for an = 8a,-1 – 16an-2 for n2 2 and ao = 1, aį = 2. Find the solution for a, = 8a,-1 – 16a„-2 for n 2 2 and ao = 5, a1 = 7. Note: This differs from the previous problem only by its initial conditions.

Solve these recurrence relations together with the initial conditions given. Recall that the solu- tion to a second order recurrence relation An = C1 An-1+ C2An-2 will be of the form f(n) = a,r" + a2r". Where r1, r2 are roots to the characteristic equation of a, and ki - kor2 kor - ki a2 = with ko = ao and kį = aj. Or if the roots are repeated, it will be of the form f(n) = a\r" + a2nr". where a = ao. Find the solution for an = 8a,-1 – 16an-2 for n2 2 and ao = 1, aį = 2. Find the solution for a, = 8a,-1 – 16a„-2 for n 2 2 and ao = 5, a1 = 7. Note: This differs from the previous problem only by its initial conditions.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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