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-5dun-5Un+1 = aun-1+п 3D0, 1,...,(1)Yun-3Bun-1un-5Yun-3 + dun-5Un+1 = Qun-1n = 0,1, ..,(2)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 = QUn-1+Bun-1un-5yun-3-dun-5This section is devoted to study the qualitative behaviors of Eq. (1). Theequilibrium point of Eq. (1) is given by11. EXACT SOLUTION OF EQ. (2) WHEN a = B =y= 6 = 1This section shows the exact solutions of the following equation:Un-1Un-5Un+1 = Un-1n = 0, 1,...,(18)Un-3 + Un-5where the initial conditions are selected to be positive real numbers.Theorem 9 Let {un}-5 be a solution to Eq. (18) and suppose that u-5а, и-4 %3D 6, и-з 3D с, и-2 %3D d, и-1 %3D е, ио 3D f. Then, for n %3D 0, 1,2, ..., thesolutions of Eq. (18) are given by the following formulas:%3De2n 2n-1II (ie +c) (ic+a)'f2n d2n-1IIT (if+ d)(id + b)'c2n e2nU8n-52n-1i=1U8n-4 =-2n-1U8n-3 =2n-IT (ic + a) I (ie + c)d2n f2nU8n-2 =II (id + b) IIT (if + d)'e2n+1 2ni=1U8n-1 =II, (ie + c)(ic + a)'U8n =IT (if + d)(id + b)'c2n+1e2n+1U8n+1 =72n+12nIT (ic + a) I, (ie + c)d2n+1 f2n+1IT (id + b) II(if + d)"=D1U8n+2 =n+1Proof.It can be easily seen that the solutions are true for n = 0. We supposethat n >0 and assume that our assumption holds for n- 1. That is,e2n-2,2n-32n-3U8n-13 =II (ie + c) (ic + a)f2n-2 d2n-32n-3II" (if + d)(id + b)c2n-22n-2U8n-12 =U8n-11 =2n-2II (ic + a) I (ie + c)d2n-2 f2n-2II (id + b) IT (if + d)e2n-12n-2U8n-10 =2n-3li=12n-2U8n-9 =T2n-2I (ie + c)(ic + a)f2n-12n-2IT(if + d)(id+b)U8n-8li=1can-1e2n-1U8n-7 =-2n-12n-2:1II (ic+ a) II (ie+c)d2n-1 f2n-1U8n-6 =2n-1II (id + b) II (if + d) From Eq. (18), one can haveU8n-7U8n-11Ugn-5 = U8n-7И8п-9 + usn-11c2n-12n – 1c2n-2 2n- 22n-3c2n-1e2n-12n-22п —1T2n-II" (ic+a) II"5<(ie+c) II1 (ic+a) II1°(ie+c)e2n -1 c2n–2II",?(ie+c)(ic+a)c2n-2 e2n – 2II (ic + a) [I, (ie + c)т2п -12n-2T?n-2(ic+a) [T?", 3 (ie+c)Ili=1i=1li=1c2n-12n-12п -1,2п -22n-1II"T (ic + a) II (ie + c)2n-2II (ic+a) II",? (ie+c) II",(ie+c)(ie+c)2n-2n-3e ll"1°(ie+c)i=1c2n-1e2n-1c2n-1e2n-2IT, (ic + a) II" (ie + c)2n-12n-2II (ic + a) IT, (ie + c) (-21(2n-2)e+cc2n-1e2n-1112п -1II (ic + a) II, (ie + c)2п -2=1e(2n-2)e+cc2n-1e2n-1e(2п — 1)е + с,2n-12n-2II" (ic + a) II1 (ie + c)i=1e2n „2n-1IT (ie + c) (ic+a)

Given that the equation un+1=un-1-un-1un-5un-3+un-5,n=0,1,…----18 has the solution given by the…

This work aims to investigate the equilibria, local stability, global attractivity and the exact solutions of the following difference equations Bun-1un-5 Un+1 = aun-1+ n = 0,1, .., (1) Yun-3 - dun-5 Bun-1un-5 Un+1 = QUn-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 u for all i = -5, -4, ..., 0, are arbitrary non-zero real numbers. We also present the numerical solutions via some 2D graphs. 2. ON THE EQUATION Uln+1 = QUn-1+ Bun-1un-5 Yun-3-bun-5 This section is devoted to study the qualitative behaviors of Eq. (1). The equilibrium point of Eq. (1) is given by 11. EXACT SOLUTION OF EQ. (2) WHEN a = B = y = 8 = 1 This section shows the exact solutions of the following equation: Un-1un-5 Un+1 = Un-1 n = 0, 1,..., (18) Un-3 + Un-5 where the initial conditions are selected to be positive real numbers. Theorem 9 Let {un}-5 be a solution to Eq. (18) and suppose that u-5 = a, u-4 = b, u-3 = c, u_2 = d, u-1 = e, uo = f. Then, for n = 0, 1, 2, ..., the solutions of Eq. (18) are given by the following formulas: n=- e2n 2n-1 II ' U8n-5 2n-1 (ie +c) (ic+ a)