Show me the steps of determine blue and all information is here This work aims to investigate the equilibria, local stability, global attractivityand the exact solutions of the following difference equationsBun-1un-5Un+1 = aUn-1+n = 0,1, ..,(1)YUn-3 - dun-5'Bun-1un-5Un+1 = aUn-1-n = 0,1, ..,(2)YUn-3 + dun-5'where the coefficients a, B, y, and & are positive real numbers and the initial con-ditions ui for all i = -5, -4, .., 0, are arbitrary non-zero real numbers. We alsopresent the numerical solutions via some 2D graphs.2. ON THE EQUATION Un+1 = aUn-1 +Bun-1un-5Yun-3-dun-5(1). TheThis section is devoted to study the qualitative behaviors of Eq.equilibrium point of Eq. (1) is given by6. EXACT SOLUTION OF EQ. (1) WHEN a =B=y= 8 = 1In this section, we investigate the exact solutions of the following rational differ-ence equationUn-1un-5Иn+1 — ит-1 +n = 0, 1, ...,(10)Un-3 - Un-5where the initial conditions are positive real numbers.Theorem 5 Let {un}n=-5be a solution to Eq. (10) and suppose that u-5 =d, u-1 = e, uo = f. Then, for n = 0, 1,2, .., theа, и-4 — б, и_з — с, и-2 —solutions of Eq. (10) are given by the following formulas:e2n c"U8n-5 =(c- e)"(a – c)n'f2n d"bn-1(d - f)"(b– d)n'cn+le2nn-1U8n-4 =U8n-3 =a" (a – c)" (c – e)"'dn+1 f2nb" (b – d)" (d- f)"'e2n+1cnU8n-2 =U8n-1 =a" (a – c)"(c – e)* 'f2n+1gnbr (b – d)"(d – f)"'cn+1 e2n+1U8nU8n+1a" (c - e)" (a – c)n+1dn+1 f2n+1b" (d – f)"(b – d)n+1*U8n+2 =Proof.It can be easily observed that the solutions are true for n = 0. We nowassume that n 0 and that our assumption holds for n – 1. That is,e2n-2 cn-1n-2(c – e)n-1(a – c)n-1'f2n-2 an-1b2-2 (d – f)n-1(b – d)a-I?U8n-13 =U8n-12 =c"e2n-2U8n-11n-1(a - c)a-1(c – e)n–1'an-1 U8n-2u8n-6U8n = U8n-2 +U8n-4 - Ug8n-6d" f2n-1bn–1(d-f)n-1 (b-d)ndn+1 f2ndn+1 f2nb" (b – d)" (d – f)"b" (b-d)"(d- f)"+f2n dnF)" (b-d)"d" f2ndn f2n-1bn-1 (d-f)n-1 (b-d)"bn-1(d+dn+1 f2nb" (b – d)" (d – f)"d" f2n+1br (b – d)" (d – f)"*br (b – d)"(d – f)n-1Other solutions can be similarly proved.

Question

Show me the steps of determine blue and all information is here This work aims to investigate the equilibria, local stability, global attractivityand the exact solutions of the following difference equationsBun-1un-5Un+1 = aUn-1+n = 0,1, ..,(1)YUn-3 - dun-5'Bun-1un-5Un+1 = aUn-1-n = 0,1, ..,(2)YUn-3 + dun-5'where the coefficients a, B, y, and & are positive real numbers and the initial con-ditions ui for all i = -5, -4, .., 0, are arbitrary non-zero real numbers. We alsopresent the numerical solutions via some 2D graphs.2. ON THE EQUATION Un+1 = aUn-1 +Bun-1un-5Yun-3-dun-5(1). TheThis section is devoted to study the qualitative behaviors of Eq.equilibrium point of Eq. (1) is given by6. EXACT SOLUTION OF EQ. (1) WHEN a =B=y= 8 = 1In this section, we investigate the exact solutions of the following rational differ-ence equationUn-1un-5Иn+1 — ит-1 +n = 0, 1, ...,(10)Un-3 - Un-5where the initial conditions are positive real numbers.Theorem 5 Let {un}n=-5be a solution to Eq. (10) and suppose that u-5 =d, u-1 = e, uo = f. Then, for n = 0, 1,2, .., theа, и-4 — б, и_з — с, и-2 —solutions of Eq. (10) are given by the following formulas:e2n c&#34;U8n-5 =(c- e)&#34;(a – c)n'f2n d&#34;bn-1(d - f)&#34;(b– d)n'cn+le2nn-1U8n-4 =U8n-3 =a&#34; (a – c)&#34; (c – e)&#34;'dn+1 f2nb&#34; (b – d)&#34; (d- f)&#34;'e2n+1cnU8n-2 =U8n-1 =a&#34; (a – c)&#34;(c – e)* 'f2n+1gnbr (b – d)&#34;(d – f)&#34;'cn+1 e2n+1U8nU8n+1a&#34; (c - e)&#34; (a – c)n+1>dn+1 f2n+1b&#34; (d – f)&#34;(b – d)n+1*U8n+2 =Proof.It can be easily observed that the solutions are true for n = 0. We nowassume that n > 0 and that our assumption holds for n – 1. That is,e2n-2 cn-1n-2(c – e)n-1(a – c)n-1'f2n-2 an-1b2-2 (d – f)n-1(b – d)a-I?U8n-13 =U8n-12 =c&#34;e2n-2U8n-11n-1(a - c)a-1(c – e)n–1'an-1 U8n-2u8n-6U8n = U8n-2 +U8n-4 - Ug8n-6d&#34; f2n-1bn–1(d-f)n-1 (b-d)ndn+1 f2ndn+1 f2nb&#34; (b – d)&#34; (d – f)&#34;b&#34; (b-d)&#34;(d- f)&#34;+f2n dnF)&#34; (b-d)&#34;d&#34; f2ndn f2n-1bn-1 (d-f)n-1 (b-d)&#34;bn-1(d+dn+1 f2nb&#34; (b – d)&#34; (d – f)&#34;d&#34; f2n+1br (b – d)&#34; (d – f)&#34;*br (b – d)&#34;(d – f)n-1Other solutions can be similarly proved.

Accepted Answer

Given equation is as follows:
un+1=un-1+un-1un-5un-3-un-5,  n=0, 1, 2,…