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The point x = 0 is a regular singular point of the given differential equation. xy" +2y'xy = 0 Show that the indicial roots r of the singularity differ by an integer. (List the indicial roots below as a comma-separated list.) r = × Use the method of Frobenius to obtain at least one series solution about x = 0. Use (23) in Section 6.3 e-SP(x) dx Y2(x) = y₁(x) dx (23) where necessary and a CAS, if instructed, to find a second solution. Form the general solution on (0, ∞). O y =x|C, sinh x + C, cosh x O y = [C₁ sin x + C₂ cos x] COS x] O y = *[C, sinh x + C, cosh x O y = x[C₁ sin x + C₂ cos x Oy=x*C, sinh x+G,

The point x = 0 is a regular singular point of the given differential equation. xy" +2y'xy = 0 Show that the indicial roots r of the singularity differ by an integer. (List the indicial roots below as a comma-separated list.) r = × Use the method of Frobenius to obtain at least one series solution about x = 0. Use (23) in Section 6.3 e-SP(x) dx Y2(x) = y₁(x) dx (23) where necessary and a CAS, if instructed, to find a second solution. Form the general solution on (0, ∞). O y =x|C, sinh x + C, cosh x O y = [C₁ sin x + C₂ cos x] COS x] O y = *[C, sinh x + C, cosh x O y = x[C₁ sin x + C₂ cos x Oy=x*C, sinh x+G,

Advanced Engineering Mathematics
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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The point x = 0 is a regular singular point of the given differential equation. xy" +2y'xy = 0 Show that the indicial roots r of the singularity differ by an integer. (List the indicial roots below as a comma-separated list.) r = × Use the method of Frobenius to obtain at least one series solution about x = 0. Use (23) in Section 6.3 e-SP(x) dx Y2(x) = y₁(x) dx (23) where necessary and a CAS, if instructed, to find a second solution. Form the general solution on (0, ∞). O y =x|C, sinh x + C, cosh x O y = [C₁ sin x + C₂ cos x] COS x] O y = *[C, sinh x + C, cosh x O y = x[C₁ sin x + C₂ cos x Oy=x*C, sinh x+G,
Transcribed Image Text:The point x = 0 is a regular singular point of the given differential equation. xy" +2y'xy = 0 Show that the indicial roots r of the singularity differ by an integer. (List the indicial roots below as a comma-separated list.) r = × Use the method of Frobenius to obtain at least one series solution about x = 0. Use (23) in Section 6.3 e-SP(x) dx Y2(x) = y₁(x) dx (23) where necessary and a CAS, if instructed, to find a second solution. Form the general solution on (0, ∞). O y =x|C, sinh x + C, cosh x O y = [C₁ sin x + C₂ cos x] COS x] O y = *[C, sinh x + C, cosh x O y = x[C₁ sin x + C₂ cos x Oy=x*C, sinh x+G,
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