Show me the steps of determine red and all information is here d" f2n-2bn-1(b – d)n-1(d – f)n-1'U8n-10e2n-1 cn-1U8n-9 =— с)п-1(с —е)п-1'-1 dn-1an-1(aU8n-8 =d)"-1(d — f)п-1'c" e2n-1hn-1(b –U8n-7 =e)n-1(a – c)n'd" f2n-1bn-1(d – f)"-1(b – d)"an-1(C -U8n-6 = -Eq. (10) gives us thatU8n-7U8n-11U8n-5 = U8n-7+U8п-9 — и8n-11c"e2n-1c"2n-2c"e2n-1an-1(c-e)n-1 (a-c)" an-1(a-c)n-1(c-e)n-1c*e2n-2an-(a-c)"-1(c-e)n-Tап-1(с — е)п-1(а — с)"e2n-1 cn-1a"-1(a-c)"-1(c-e)n-Ie2n-2 naп-1(с - е)"-1 (а — с)" (! — 1)e2n-1 cn+1aп-1(с — е)"(а — с)"c"e2n-1an-(с — е)п-1(а —c)nc"e2n-1ап-1(с — е)п-1(аc)ne2n cnап-1(с — е)"(а — с)"Moreover, it can be seen from Eq. (10) thatU8n-6U8n-10Usn-4 = usn-6 +и8п-8 — и8п-10d" f2n-1bn-1(d-f)n-1 (b-d)n bn-1(b-d)n-1(d-f)n-If2n-1dn-1d" f2n-2d" f2n-1bn-1(d — f)n-1(b — d)пd" f2n-2bn-1 (b-d)n-1(d-f)"-I¯ br–1 (b-d)n-1(d-f)n-Id" f2n-2d" f2n-1bn-1(d – f)n-1(b – d)"fn-1(d – f)n-1(b – d)" (à – )dn+1 f2n-1bn-1(d – f)"(b – d)"d" f2n-1bn-1(d – f)n-1(b – d)nf2n drbn-1(d – f)"(b – d)"¨ 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

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Show me the steps of determine red and all information is here d&#34; f2n-2bn-1(b – d)n-1(d – f)n-1'U8n-10e2n-1 cn-1U8n-9 =— с)п-1(с —е)п-1'-1 dn-1an-1(aU8n-8 =d)&#34;-1(d — f)п-1'c&#34; e2n-1hn-1(b –U8n-7 =e)n-1(a – c)n'd&#34; f2n-1bn-1(d – f)&#34;-1(b – d)&#34;an-1(C -U8n-6 = -Eq. (10) gives us thatU8n-7U8n-11U8n-5 = U8n-7+U8п-9 — и8n-11c&#34;e2n-1c&#34;2n-2c&#34;e2n-1an-1(c-e)n-1 (a-c)&#34; an-1(a-c)n-1(c-e)n-1c*e2n-2an-(a-c)&#34;-1(c-e)n-Tап-1(с — е)п-1(а — с)&#34;e2n-1 cn-1a&#34;-1(a-c)&#34;-1(c-e)n-Ie2n-2 naп-1(с - е)&#34;-1 (а — с)&#34; (! — 1)e2n-1 cn+1aп-1(с — е)&#34;(а — с)&#34;c&#34;e2n-1an-(с — е)п-1(а —c)nc&#34;e2n-1ап-1(с — е)п-1(аc)ne2n cnап-1(с — е)&#34;(а — с)&#34;Moreover, it can be seen from Eq. (10) thatU8n-6U8n-10Usn-4 = usn-6 +и8п-8 — и8п-10d&#34; f2n-1bn-1(d-f)n-1 (b-d)n bn-1(b-d)n-1(d-f)n-If2n-1dn-1d&#34; f2n-2d&#34; f2n-1bn-1(d — f)n-1(b — d)пd&#34; f2n-2bn-1 (b-d)n-1(d-f)&#34;-I¯ br–1 (b-d)n-1(d-f)n-Id&#34; f2n-2d&#34; f2n-1bn-1(d – f)n-1(b – d)&#34;fn-1(d – f)n-1(b – d)&#34; (à – )dn+1 f2n-1bn-1(d – f)&#34;(b – d)&#34;d&#34; f2n-1bn-1(d – f)n-1(b – d)nf2n drbn-1(d – f)&#34;(b – d)&#34;¨ 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

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