The point x = O 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) = y,(x) dx (23) where necessary and a CAS, if instructed, to find a second solution. Form the general solution on (0, o).

The point x = O 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) = y,(x) dx (23) where necessary and a CAS, if instructed, to find a second solution. Form the general solution on (0, o).

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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Question

The point x = 0 is a regular singular point of the given differential equation.
ху" + 2у' — ху %3D0
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
Y2(x) = Y1(x) /
e-SP(x) dx
dx
(23)
where necessary and a CAS, if instructed, to find a second solution. Form the general solution on (0, 0).
1
C, sin x + C, cos x
O y = -
O y = x C, sinh x + C, cosh x
O y = xC, sin x + C, cos x
1
O y =C, sinh x + C2 cosh
O y = x2 C, sinh x + C,

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