Find the eigenvalues ,, and eigenfunctions y(x) for the given boundary-value problem. (Give your answers in terms of n, making sure that each value of ncorresponds to a unique eigenvalue.);y"+2y+ (+1)y= 0, y(0)= 0, y(4) = 0(No Response) - 1, 2, 3,Y(x)(No Response) ne 1, 2, 3,...

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Answered: Find the eigenvalues ,, and…

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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Please do number 5
3
[3] [4] [¹]. Let Suppose the eigenvalues of a (3 × 3) matrix A are 2, −1/2, and 1/3, with corresponding eigenvectors Let x = []. Find the solution of the equation *k+1 = Ark for the specified o= xo, and describe what happens as ko. You may use a calculator to perform row reduction.
Use eigenvalue metnoa to nna requirea solution of the following system. x₁ x2 = −4x₁3x2 – £3 and - x3 = 2x1 + x2 = x3 O = = 4x₁ + 4x2 + 2x3. The initial conditions are ₁ (0) = 0, x2 (0) = 1 and 3 (0) = 4. 2 -8-8-0 -2 + sin 2t -2 +e² 3 7 x(t) = cos 2t 6 6 4 2 H H+O -5 +e²t 4 3 x(t) = cos 3t -3 + sin 3t x(t) = cos 3t x(t) = cos 2t 2 -#-#-D -2 + sin 3t 3 4 2 -6 -4 + sin 2t 6 3 2 tel + e 0
Solve
mm.2
and Vz - 2 arp eigenved ors pf motrx A cor fespontng to ergenvalno d, = -5 and do =5 A (vi + Vz ) = to A (sT; ) = ?
Apply the eigenvalue method to solve the initial value problem
in pic
5. Apply the eigenvalue method to find the general solution of the given system. Fina diso ahe corresponding particular solution by using the initial values. (x = 9x1 + 5x2 x½ = -6x1 – 2x2 Initial: x, (0) = 1,x2(0) = 0
PART 1 (MCQ: 8 Marks): 1. Choose the most appropriate answer. (a) The eigenvalues of the following eigenvalue problem: are given by An = 0 = (1),X = (0),x '0= xY+ „X (A) n², n=0, 1, 2, 3, - - - (C) (na)², n = 0,1, 2, 3, · - . (B) n², n=1,2,3, - - - (D) (n7)², n= 1, 2, 3, · - - (b) At x = 0, the Fourier series of x - 2, = (x)f I 5x > 0 converges to: (A) -2 (B) –1 (D) 1 (c) The solution of the following Cauchy problem: '00 > x > - u(x, 0) = 0, 4 (x, 0) = x, *00 > x > o0- is given by u(x, t) = (A) [(z+ t)? – (2 – t)*] = ct (B) (7 + t) + (x – t)] =: (C) (z +t)² + (x – t)*] = (2² + t*) 1=(9-2) -0+0)은 (a) (d) Let o(x) = x² + x, x > 0. If defines an even extension of ø to the entire real line, then for x < 0, (x) = (C) -a2 +x (A) x² +x X - „x ()
Find the eigenvalues , and eigenfunctions y(x) for the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.) y" + 2y +(2+1)y = 0, y(0) = 0, y(9) = 0 Yn(x) = 2 ²n² 18 Need Help? Read It n = 1, 2, 3, ... n = 1, 2, 3,...

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Find the eigenvalues ,, and eigenfunctions y(x) for the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.); y"+ 2y (+1)y = 0, y(0) = 0, y(4) = 0 (No Response) - 1, 2, 3, Y(x) (No Response) n 1, 2, 3,...