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
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?
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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