Explain the determine red and the inf is here There exist two positive distinctive real numbers P and Q representing twopositive roots of Eq.(4.19) such that[(a1 + a3 + a5) – (a2 + a4)] + 8P =(4.21)2 [(B1 + B3 + B5) + A (B2 + B4)]and[(a1 + a3 + a5) – (a2 + a4)] – 82 [(81 + B3 + B5) + A (82 + B4)](4.22)where8 = V[(a1 + a3 +a5) – (a2 + a4)]² – n,and4 [(a1+ a3 + a5) – (a2 + a4)] [(ß1 + B3 + B5) (œ2 + a4) + A (B2 + B4) (a1 + a3 + a5)][((32 + B4) – (B1 + B3 + B5)) (A + 1)]Now, let us prove that P and Q are positive solutions of prime period two ofEq.(1.1). To this end, we assume that y-5 = P, y-4 = Q, y–3 = P, y-2 =Q, y-1 = P, Yo= Q. Now, we are going to show that Yı = P and y2 = Q.From Eq.(1.1) we deduce thatа1у-1 + ӕ2у-2 + азу-з + аду-4 + 05у-5Y1 = Ayo +B1y-1 + B2y-2 + B3y-3 + B4Y-4 + B5Y-5(@1 + a3 + a5) P+ (a2+ a4) Q= AQ +(4.23)(B1 + Вз + В5) Р + (82 + Вa) Q Substituting (4.21) and (4.22) into (4.23) we deduce thatАQ +(с1 + аз + as)Р+ (а2 + а4) Q- PУ1 — Р —(B1 + Вз + B5) Р+ (32 + Ва) Q[A (B1 + B3 + B3) – (B2 + Ba)]PQ + A (B2 + B4) Q² – (B1 + ß3 + B5) P²(B1 + B3 + B5) P+(B2+ B4) Q(a1 + a3 + a5) P+(@2+ a4) Q(B1 + B3 + B5) P+(82+ B4) Q([A(B1+33+Bs)-(82+B4)][S1][(B1+33+B5)(@2+a4)+A(82+B4) (ai+a3+a5)][(81+33+B5)+A(82+34)]²[((82+B4)-(ß1+B3+B5))(A+1)](B1 + B3 + B5)[(a1+a3+a5)-(a2+a4)]+ô2[(B1+B3+B5)+A(B2+B4)]+ (B2 + B1) (aita3tas)-(a2ta4)]-82[(B1+B3+B3)+A(82+B4)]2[(@1+a3+a5)-(a2+a4)]-8A (B2 + B4) ( 2(31+83+Bs)+A(B2+B4)](a1ta3+as)-(a2ta4)]+ô\²2[(31+33+ßs)+A(B2+B4)](B1 + B3 + B5)+ (B2 + Ba) ( laita3+a5)-(ag+a4)]-8)2[(B1+83+B5)+A(B2+B4)][(@1+a3+ag)-(a2+a4)]+8`2[(81+B3+B5)+A(B2+B4)] .[(a1+a3+a5)-(a2+a4)]+8`2[(B1+33+B5)+A(32+B4)](B1 + B3 + B5)(a1 + a3 + a5)++ (a2 + a4)[(a1+a3+a5)-(a2+a4)]-ô2[(81+B3+B3)+A(B2+B4)] )(B1 + B3 + B5)[(a1ta3+a5)-(a2+a4)]+82[(B1+33+B5)+A(82+B4)]+ (B2 + Ba) ( ata3+a;)-(ag+a4)]-82[(31+B3+Bs)+A(B2+B4)](4.24)

Name: Explain the determine red and the inf is here There exist two positive
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Description: Explain the determine red and the inf is here There exist two positive distinctive real numbers P and Q representing twopositive roots of Eq.(4.19) such that[(a1 + a3 + a5) – (a2 + a4)] + 8P =(4.21)2 [(B1 + B3 + B5) + A (B2 + B4)]and[(a1 + a3 + a5) –

The given values of roots: Given y1:

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(ai + a3 + a5) P+ (@2+ a4) Q (B1 + B3 + B3) P+ (B2 + B4) Q [A (B1 + B3 + B5)- (B2+ B4)]PQ + A (82 + B4) Q2 - (B1 + B3 + B5) P2 Y1 – P = AQ + - P | | (B1 + B3 + B5) P + (B2 + B4) Q (a1 + a3 + a5)P+ (a2+ a4) Q + (B1 + B3 + B5) P+ (82+ B4) Q

(ai + a3 + a5) P+ (@2+ a4) Q (B1 + B3 + B3) P+ (B2 + B4) Q [A (B1 + B3 + B5)- (B2+ B4)]PQ + A (82 + B4) Q2 - (B1 + B3 + B5) P2 Y1 – P = AQ + - P | | (B1 + B3 + B5) P + (B2 + B4) Q (a1 + a3 + a5)P+ (a2+ a4) Q + (B1 + B3 + B5) P+ (82+ B4) Q

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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