Find the first four nonzero terms in a power series expansion of the solution to the given initial value problem. 6y'-5e²xy=0; y(0) = 1 ∞ Rewrite the given differential equation in terms of a power series, using a general solution y(x)= Σ an (x-xo)". Expand e²x 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. Ο.Α. 6 Σ n(n-1)an (x-xο) "-2-5( n=2 +...) Σ an(x-x)" =0 n=0 00 00 ○ B. 6 Σ n(n-1)a (x-x)n-²-5( _ +...) Σ na (x-xò) ª−1=0 n=2 n=1 O c. 6(+) Σ nan (x-xo)n-1-5 Σan (x-x)=0 n=1 n=0 ∞ ✅D. 6 ¶ na, (x-x)n−1−5[1+2x+ 2x² + 3x³ +..) [ ³₂ (x-x)² =0 Σ Σan n=1 n=0 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. 6y'-5e²xy=0; y(0) = 1 ∞ Rewrite the given differential equation in terms of a power series, using a general solution y(x)= Σ an (x-xo)". Expand e²x 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. Ο.Α. 6 Σ n(n-1)an (x-xο) "-2-5( n=2 +...) Σ an(x-x)" =0 n=0 00 00 ○ B. 6 Σ n(n-1)a (x-x)n-²-5( _ +...) Σ na (x-xò) ª−1=0 n=2 n=1 O c. 6(+) Σ nan (x-xo)n-1-5 Σan (x-x)=0 n=1 n=0 ∞ ✅D. 6 ¶ na, (x-x)n−1−5[1+2x+ 2x² + 3x³ +..) [ ³₂ (x-x)² =0 Σ Σan n=1 n=0 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
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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.
6y' - 5e²xy=0; y(0) = 1
00
Rewrite the given differential equation in terms of a power series, using a general solution y(x) = Σan (x-xo)". Expand e²x 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
○ A. 6 Σ n(n-1)a, (x-xo)n-²-5(
n=2
00
00
B. 6 Σ n(n-1)an (x-x₁)n-²-5( + ...) Σ na, (x−×。)'
n=2
n=1
00
+ ...) Σ ªn (x-x₁) = 0
n=0
∞
00
○ c. 6(+) Σ na, (x-xo)n-1-5 Σan (x-xo) n = 0
n=1
n=0
∞0
+
+ ...
4
D. 6
6 Σnan (x-x₁)n-1 -5 1+2x+ 2x² + - 3 + ³ + ...).
n=1
y(x) =
(Type an expression that includes all terms up to order 3.)
¹ = 0
∞
Σan (x-xo) n = 0
n=0
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