Use the method of Frobenius and a reduction of order procedure to find the first three nonzero terms in the series expansion about the irregular singular point x=0 for a general solution to the differential equation x²y" +4y¹-2y=0. Let y₁ (x) and y2(x) be two linearly independent solutions. Write the general solution y(x) using the first three terms of y₁ (x) and at most the first three terms of y2 (x). -1 _x00- & [1 + x + 2) +G₂(x² + x^² +‡) ² y(x)= C₁ 1+ ½ -3 +C 5' (Type an expression in terms of C₁ and C₂.)
Use the method of Frobenius and a reduction of order procedure to find the first three nonzero terms in the series expansion about the irregular singular point x=0 for a general solution to the differential equation x²y" +4y¹-2y=0. Let y₁ (x) and y2(x) be two linearly independent solutions. Write the general solution y(x) using the first three terms of y₁ (x) and at most the first three terms of y2 (x). -1 _x00- & [1 + x + 2) +G₂(x² + x^² +‡) ² y(x)= C₁ 1+ ½ -3 +C 5' (Type an expression in terms of C₁ and C₂.)
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:w(r,x)= Σax"+
α
n=0
w"(r,x)=
n=0
w'(r,x)= Σ(n+r)axt
Σ(n+r-1)(n+r)a_r*+-2
η
n=0
η
n+r-1
![Use the method of Frobenius and a reduction of order procedure to find the first three nonzero terms in the series expansion about the irregular singular point x=0 for a general solution to the differential equation
x²y" +4y' -2y=0.
Let y₁ (x) and y2(x) be two linearly independent solutions. Write the general solution y(x) using the first three terms of y₁ (x) and at most the first three terms of y2 (x).
(29=9(1}x}2) «Q[**8²16)
y(x) = C₁ 1+
~₁ [1 + 1⁄² x + ² x ²] + C₂² ( x ²°
+X
5
(Type an expression in terms of C₁ and C₂.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F511d779c-bf10-4315-98b1-4f0038c55113%2F3e2e53d4-a4c9-45c2-84c0-4d351939d534%2Ft9xql88_processed.png&w=3840&q=75)
Transcribed Image Text:Use the method of Frobenius and a reduction of order procedure to find the first three nonzero terms in the series expansion about the irregular singular point x=0 for a general solution to the differential equation
x²y" +4y' -2y=0.
Let y₁ (x) and y2(x) be two linearly independent solutions. Write the general solution y(x) using the first three terms of y₁ (x) and at most the first three terms of y2 (x).
(29=9(1}x}2) «Q[**8²16)
y(x) = C₁ 1+
~₁ [1 + 1⁄² x + ² x ²] + C₂² ( x ²°
+X
5
(Type an expression in terms of C₁ and C₂.)
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