1. Which of the following power series must be used as the nonhomogeneous part for the given initial value problem y" – y' + (x + })° y = In (} + x) { y (-}) = 1, y' (-}) = 0 in order to obtain the solution by power series solution method? (-1)" (x – B) -1)"+' (x)n n! C) (-1)"+1 (2x + 1)" n=0 n=1 n n=0 (-1)"-' (x + })"| E) (-1)"x" ( 2"(n + 1) n=1 n=1 IM8

1. Which of the following power series must be used as the nonhomogeneous part for the given initial value problem y" – y' + (x + })° y = In (} + x) { y (-}) = 1, y' (-}) = 0 in order to obtain the solution by power series solution method? (-1)" (x – B) -1)"+' (x)n n! C) (-1)"+1 (2x + 1)" n=0 n=1 n n=0 (-1)"-' (x + })"| E) (-1)"x" ( 2"(n + 1) n=1 n=1 IM8

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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1. Which of the following power series must be used as the nonhomogeneous part for the given initial value problem { y" – y + (x + }) y = In ({ + x) y (-}) = 1, y' (-}) = 0 in order to obtain the solution by power series solution method? A) -1)" (x – )" (-1)"+1 (x)" B) (-1)"+1 (2x + 1)" n! n=0 n=1 n=0 (-1)"-' (x + })" (-1)" x" E) 2" (n + 1) n=1 n=1
Solve the initial-value problem y" + xy' + y = 0, y(0) = 0, y'(0) = 1 in the form of a power series in powers of x. (- 1)" 2n n! x2n + 1 O A. y = > (2n + 1)! n=0 (- 1)A 2ª (n + 1)! x2n +1 (2n + 1)! O B. y = > n=0 (-1)" 2n +1 n! x 2n + 1 (2n + 1)! O C.y = > n=0 (- 1)n +1 2n n! x2n + 1 O D. y = > (2n + 1)! n=0 (- 1)a 2º (n - 1)! x2n + 1 E. y = > n=0 (2n + 1)!
Find two power series solutions of the given differential equation about the ordinary point x = 0. (x2+1)y" 6y = 0 Oy₁ = 1 + 3x² + x²-to 1,6 Oy₁ = 1 + 3x² + 5x4 + 7x6 + Oy₁ = 1 + 3x² + x4 + +6 5 + + and y₂ = x + x³ and Y2 = x + 2x³ + 3x5 + 4x7. and y₂ = x - x³ 34 ₁=1+²+x+6+ ... and y₂ = x+3x² Oy₁ = 1 - 3x² + 5x4 – 7x6 + and y₂ = x - 2x³ + 3x5 - 4x² + .
12a
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