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
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,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F73319230-166d-492d-bd14-825bd824c3a2%2F8dc10511-7253-428f-997e-43578b419ca5%2Fpg46reg_processed.png&w=3840&q=75)
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,
![](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F73319230-166d-492d-bd14-825bd824c3a2%2F8dc10511-7253-428f-997e-43578b419ca5%2Fjts31o_processed.jpeg&w=3840&q=75)
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