2(0) Find the smallest positive Solution of the Systemof linearPrear Congruencesx = 1 (mod 7)X =7 (mod 87²²² → x = 7 (mod 2) → x = 1 moe4 (mod 27)³² → X= 4(mod 3) → X=IM=415

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Answered: 2(b) Find the smallest positive…

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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Theorem 1. The following system of equations Un-1Vn-3 Un-3Vn-1 Un+1 = and vn+1 = (35) Vn-1(A+ Bun-1Vn–3) Un-1(C+ Dun-3Vn–1)' (1-А) has a 2-periodic solution if u_3 = u_1, v_3 = v_1, u_3v_3 = u_2v_2 = " and A = 42 C, B = D+ 0. 41 -A), where A = C,B = Proof. Let u _3 = u_1,v_3 = v_1 and u_3v_3 = u_2v_2 = D in the exact equation (34a). Then 2m-1 2m + (1-C) Σ C n-1 l=0 U4n-2 =u-2 |T 2m A2m+1 + (1– A) E A! m=0 1=0 =u-2. (36)
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6. It is known that the general solution of the system *- )* = x is given by e³t+ [¹1] = C1 Use the method of Undetermined Coefficients for systems to find the form of a particular solution to the nonhomogeneous system x': A. x₂(t) = te a+eb+tc+d (B.x₂(t) = = teta+tb+c C. xp(t) = ea + e³t b+tc+d D. xp(t) = tea+t²b+tc+d E. x₂(t) = t'e' a+e¹b+tc+d = et. x+ 4e² Le+ Xce)= (ater ) t b, It = te¹ A + TB + C IB

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2(b) Find the smallest positive Solution of the System of linear Congruences X = 1 (mod 7) X = 7 (mod 87²² → x = 7 (mod 2) → x = 1 moe 4 (mod 277¹³ →→ X= 4(mod 3) →> x = 1mc