4. Find the first four successive approximations u(¹)(t,a), u(²)(t,a),u³(t, a), and u(4) (t, a) for the systemİl = −X1#2 = −x2+x}*3 = x3 + x².İçShow that u(3) (t, a) = u(4) (t, a)Find S and U for this problem.=...and hence u(t, a) :=u(³) (t, a).

Ans- To find the successive approximations, we first need to write the system in normal…

Answered: 4. Find the first four successive…

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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Write the given system in the form x' = P(t)x+ f(t). x' = 3x-7y+z+t y' = x-5z+t²2² z' = 3y - 5z+t³ ---
4. Let (*) be the following homogeneous system F: of (n-1) linear equations in n unknows All X₁ + A₁₂ X₂ t + An Xn = 0. a22X2 A21X₁ + a₂₂X₂ + ... + Cl₂n Xn = 0. An-1,1X₁+ an-1, 2X₂ + + On-in Xn = 0. ,2 Is Suppose that no equation in this system linear combination of the other equations. For each =1,2,.nlet Ai & Ma-x) (F) be the matrix obtained by deleting the ith column of the coefficient matrix of (*), and let det (Ai). Ci over it! = (*) (-1) Prove the following statements (a) Not all of C₁,..., Cn are 0. (5) The solution space of the system (*) is olle-dimen (C) A vector (X₁. --, Xn) € F" is a -sional, solution to the system (*) iff (X₁...., Xn) = t (C₁, , (n) a ***/ for some te F.
Solve for x and y the following system of simultaneous equations 2 In(x) = In(y) + In(9) e*ev = e3 subject to the restriction on x and y that x > 0, y > 0. a. Not in the list b. x=(9-/189)/2, y=(-15+/189)/2 C. x=(-9+/189)/2, y=(15-/189)/2 d. x=(-9-/189)/2, y=(-15-/189)/2
Show that all solutions of the system - (: )- a x' : d approach zero as t → o if and only if a +d 0.

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4. Find the first four successive approximations u(¹)(t,a), u(²)(t,a), u³(t, a), and u(4) (t, a) for the system *₁ -I1 İ₂ = −x2 + x² *3 = x3 + x². Show that u(3) (t, a) = u(4) (t, a) Find S and U for this problem. and hence u(t, a) = u(³) (t, a).

4. Find the first four successive approximations u(¹)(t,a), u(²)(t,a), u³(t, a), and u(4) (t, a) for the system ₁ -I1 İ₂ = −x2 + x² 3 = x3 + x². Show that u(3) (t, a) = u(4) (t, a) Find S and U for this problem. and hence u(t, a) = u(³) (t, a).