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Use the method of Frobenius to obtain two linearly independent series solutions about x 0. Form the general solution on (0, 0). 9a?y" + 9x?y' + 2y = 0 O ri = , r2 = y (2) = C; zi (1- z +-t... ] + C,zi [1-2+ -+...] 120 On=-, n=- y (2) %3 Cizi [1+글a+ 옮2 + 10+..] + Caai [1+ 글2+ 고2 + 23 +..] On=, n=- y (2) = C,ri (1- + . ] + C (1+++ ..] 120 Orn =-, r2 = y (2) = C;z [-1+ =-+ ] + C,zi (1-- - .] %3D

Use the method of Frobenius to obtain two linearly independent series solutions about x 0. Form the general solution on (0, 0). 9a?y" + 9x?y' + 2y = 0 O ri = , r2 = y (2) = C; zi (1- z +-t... ] + C,zi [1-2+ -+...] 120 On=-, n=- y (2) %3 Cizi [1+글a+ 옮2 + 10+..] + Caai [1+ 글2+ 고2 + 23 +..] On=, n=- y (2) = C,ri (1- + . ] + C (1+++ ..] 120 Orn =-, r2 = y (2) = C;z [-1+ =-+ ] + C,zi (1-- - .] %3D

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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Use the method of Frobenius to obtain two linearly independent series solutions about x 0. Form the general solution on (0, 0). 9x?y" + 9x?y' + 2y = 0 O ri = 3, r2 = y (2) = C; 23 [1 – ža + -+...] + Cza [1- + - ...] 3 120 Orn = -, =- y (2) = C} 2 (1 +e +++...] +C,2 [1++ +t..] 3 7 120 On =, r =- y (2) = C, 2 [1 – + -+...]+C2a [1+e+ + t..] r2 = - 2² -+...] + C2x + x - 1] 120 O ri = -, r2 y (2) = C,23 [(-1+ }r -+.. ] +C2zi (1- - - ..] 120 113
Transcribed Image Text:Use the method of Frobenius to obtain two linearly independent series solutions about x 0. Form the general solution on (0, 0). 9x?y" + 9x?y' + 2y = 0 O ri = 3, r2 = y (2) = C; 23 [1 – ža + -+...] + Cza [1- + - ...] 3 120 Orn = -, =- y (2) = C} 2 (1 +e +++...] +C,2 [1++ +t..] 3 7 120 On =, r =- y (2) = C, 2 [1 – + -+...]+C2a [1+e+ + t..] r2 = - 2² -+...] + C2x + x - 1] 120 O ri = -, r2 y (2) = C,23 [(-1+ }r -+.. ] +C2zi (1- - - ..] 120 113
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