Find the first four nonzero terms in a power series expansion of the solution to the given initial value problem. 5y' - 3e³xy=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 ³x 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 OA. 50 00 ∞0 +..) Σ nan (x-xo)n-1-3 Σ an (x-xo) n=0 n=1 n=0 ∞0 Ο Β. 5 Σ n(n-1)an (X-Xo)n-2-3( n=2 ∞0 ο c. 5 Σ n(n-1)an (x-xο)n-2-3( n=2 +...) Σ. nan (X-X0)n-1=0 n=1 +...) Σ an(x-xD)"=0 n=0 (...) ∞0 00 O D. 5 Σ. nan (x-x0) 0-1-3( +...) Σ an (x-xo)"=0 n=1 n=0
Find the first four nonzero terms in a power series expansion of the solution to the given initial value problem. 5y' - 3e³xy=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 ³x 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 OA. 50 00 ∞0 +..) Σ nan (x-xo)n-1-3 Σ an (x-xo) n=0 n=1 n=0 ∞0 Ο Β. 5 Σ n(n-1)an (X-Xo)n-2-3( n=2 ∞0 ο c. 5 Σ n(n-1)an (x-xο)n-2-3( n=2 +...) Σ. nan (X-X0)n-1=0 n=1 +...) Σ an(x-xD)"=0 n=0 (...) ∞0 00 O D. 5 Σ. nan (x-x0) 0-1-3( +...) Σ an (x-xo)"=0 n=1 n=0
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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Transcribed Image Text:Find the first four nonzero terms in a power series expansion of the solution to the given initial value problem.
5y' - 3e³xy=0; y(0) = 4
∞0
Rewrite the given differential equation in terms of a power series, using a general solution y(x) = Σ a₁(x-x₁) n. Expand ³x 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
∞
OA. 50 - ...) Σ nan (x-xo)"-1-3 Σ an(x-xo)" =0
n=1
n=0
00
O B. 5 Σ n(n-1)a, (x-xo) n−² − 3 (
n=2
∞0
+ ...) Σ nan (x-x₁)n-1=0
n=1
00
∞0
0 c. 5 Σ n(n-1)an (x-xο)n-2-3( +...) Σ an (x-x)" =0
n=2
n=0
00
∞0
O
D. 5 Σ. nan (x-x)"-1-3( +...) Σ an (x-x)"=0
n=1
n=0
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