Find the first four nonzero terms in a power series expansion of the solution to the given initial value problem. 2y'-exy=0; y(0) = 4 00 Rewrite the given differential equation in terms of a power series, using a general solution y(x)= Σan (x-xo)". Expand ex in a power series, writing the first four terms. Select the correct n=0 answer below and fill in the answer box to complete your choice. ∞ O A. 2(+) Σ na, (x-xo)n-1- Σan (x-xo) "=0 n=1 n=0 • Β. nan B. 2 Σ nª, (X-X)^-1-1. n=1 x²x³ 1+x+ + 2 6 + ... Σan (x-x) = 0 n=0 n=0 00 00 ○ c. 2 Σ n(n-1)a (x-x)^−2 − ( + ...) Σ ªn (x-xo)^=0 n=2 n=0 ∞ ∞ ○ D. 2 Σ n(n-1)a (x-x₁)ñ−² − ( _ + ---) Σ na, (x-xò)n-¹=0 n=2 n=1 C y(x) = +... (Type an expression that includes all terms up to order 3.)
Find the first four nonzero terms in a power series expansion of the solution to the given initial value problem. 2y'-exy=0; y(0) = 4 00 Rewrite the given differential equation in terms of a power series, using a general solution y(x)= Σan (x-xo)". Expand ex in a power series, writing the first four terms. Select the correct n=0 answer below and fill in the answer box to complete your choice. ∞ O A. 2(+) Σ na, (x-xo)n-1- Σan (x-xo) "=0 n=1 n=0 • Β. nan B. 2 Σ nª, (X-X)^-1-1. n=1 x²x³ 1+x+ + 2 6 + ... Σan (x-x) = 0 n=0 n=0 00 00 ○ c. 2 Σ n(n-1)a (x-x)^−2 − ( + ...) Σ ªn (x-xo)^=0 n=2 n=0 ∞ ∞ ○ D. 2 Σ n(n-1)a (x-x₁)ñ−² − ( _ + ---) Σ na, (x-xò)n-¹=0 n=2 n=1 C y(x) = +... (Type an expression that includes all terms up to order 3.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Find y(x)
Transcribed Image Text:Find the first four nonzero terms in a power series expansion of the solution to the given initial value problem.
2y'exy=0; y(0) = 4
00
Rewrite the given differential equation in terms of a power series, using a general solution y(x) = Σan (x-xo)". Expand ex in a power series, writing the first four terms. Select the correct
answer below and fill in the answer box to complete your choice.
n=0
∞0
00
○ A. 2( +...) Σ nan (x-x₁)n-1 - Σ an (x-xo) n = 0
n=1
n=0
00
B. 2 Σ na, (x-x₁)n-1
n(x-x)^-1-
n=1
∞0
ο c. 2 Σ n(n-1)an (X-Xo) n-2- (
n=2
1+X+ +
00
O D. 2 Σ n(n-1)a (x-xo) n−² − (
n=2
x² x³
2 6
+ ...
+ ...
∞0
Σan (x-x₁) = 0
n=0
00
+...) Σ *(x-X0) π
n=0
(x-x₁) = 0
00
+ ...) Σ na, (x-x₁) n − 1 = 0
n=1
y(x) =
(Type an expression that includes all terms up to order 3.)
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