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Consider the initial value problem y" -xy' -y=0; y(0) = 0, y'(0) = 1 The differential equation has power series solution y = Σ ax" n=0 (a) The recurrence relation among the coefficients is OA OB. O C. O D. an n+1 an+2=an+1+an for n²0 an+1 = OB. an+2= an n+2 for n20 an+1 n n+1 OE. None of the given answers is correct y=a1+x+ (b) The general solution of the DE has the form OA -) + ²₁ (x + CA. for nz 0 a, for n20 +X+ 2 2 + 2 x² y=a1++ 2 8 OC. yao(1+x² + x³ + ....) + a₁ (x+x² + 2x³ + ...) OD. 4 X + x²x³ 3 3 x² X +- y=ao 2 6 OE. None of the given answers is correct + X+ 3 + 5 (c) The first three terms of the power series solution of the initial value

Consider the initial value problem y" -xy' -y=0; y(0) = 0, y'(0) = 1 The differential equation has power series solution y = Σ ax" n=0 (a) The recurrence relation among the coefficients is OA OB. O C. O D. an n+1 an+2=an+1+an for n²0 an+1 = OB. an+2= an n+2 for n20 an+1 n n+1 OE. None of the given answers is correct y=a1+x+ (b) The general solution of the DE has the form OA -) + ²₁ (x + CA. for nz 0 a, for n20 +X+ 2 2 + 2 x² y=a1++ 2 8 OC. yao(1+x² + x³ + ....) + a₁ (x+x² + 2x³ + ...) OD. 4 X + x²x³ 3 3 x² X +- y=ao 2 6 OE. None of the given answers is correct + X+ 3 + 5 (c) The first three terms of the power series solution of the initial value

Advanced Engineering Mathematics
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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5please show written work can you also show me the frost three terms of the series?
Consider the initial value problem y" -xy' -y=0; y(0) = 0, y'(0) = 1 The differential equation has power series solution y = Σ a,x" Ë n=0 (a) The recurrence relation among the coefficients is ОА OB. O C. O D. an n+1 an+2=an+1+an for n²0 an+1 = OB. an+2= an n+2 an+1 n+1°h OE. None of the given answers is correct (b) The general solution of the DE has the form OA x²x³ 3 y=a1+x+ 2 for n20 a, for n20 X for nz 0 +X+ x² 2 2 + 4 X y=a1++ + ...+ ₁1 (x+ X+ 2 8 OC. y=ao (1+x² + x³ + ....) + a₁ (x+x² + 2x³ + ...) OD. + a₁ x + x² X y=ao +- + 2 6 OE. None of the given answers is correct 3 3 5 + (c) The first three terms of the power series solution of the initial value problem is
Transcribed Image Text:Consider the initial value problem y" -xy' -y=0; y(0) = 0, y'(0) = 1 The differential equation has power series solution y = Σ a,x" Ë n=0 (a) The recurrence relation among the coefficients is ОА OB. O C. O D. an n+1 an+2=an+1+an for n²0 an+1 = OB. an+2= an n+2 an+1 n+1°h OE. None of the given answers is correct (b) The general solution of the DE has the form OA x²x³ 3 y=a1+x+ 2 for n20 a, for n20 X for nz 0 +X+ x² 2 2 + 4 X y=a1++ + ...+ ₁1 (x+ X+ 2 8 OC. y=ao (1+x² + x³ + ....) + a₁ (x+x² + 2x³ + ...) OD. + a₁ x + x² X y=ao +- + 2 6 OE. None of the given answers is correct 3 3 5 + (c) The first three terms of the power series solution of the initial value problem is
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