q13a - i/l S'WW QUIZZ 13 MATH 2233 SECTION 2, SPRING 2011...

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Unformatted text preview: i/l S'WW QUIZZ 13 MATH 2233 SECTION 2, SPRING 2011 INSTRUCTOR: WEIPING LI Print Name and Student # SHOW WORK FOR CREDIT !!! SHOW WORK FOR CREDIT H! (1) (10pts) The differential equation is given by 31:23]” + 2301;, —|— mzy = O. (a) Show that the given differential equation has a regular singular point at a: = O . , ..L FOO: fig irx)‘ 53> ‘ .-‘v i._3;— (Wm X2": 0 XIX/(‘3 X (X) b2LZV‘oX3X D 3 2 5;;70 i“ X : o is mitten/V (b) Determine the indicial equation and the root of the indicial equation. Llecmi) Ewe/914 $3 ’r(Y—i)+%-3’+ O :— O 2 WEIPING LI (2) (10pts) A differential equation has roots T1 = 1/3 and 7‘2 = O of its indicial equation at a regular singular point :50 = 0. Given the recurrence relation an—l (n + r)[3(n +7“) — 1] ' (a) Find the first three nonzero terms of the series solution corresponding to the larger root. an:— Y=“'L ._ ._ a"'l : —— am" i 5— a" ' (hf‘é)(3n+5<é~i) (Sm—H) ’1 ca a9 a _“a0 :— _.._l_§: ’ 4+ I 42 7 a 7-4 2 a 1,. Q7. : __ . a0 5 10.5 {07-45 2 Y t 3 l Hex (QBTCMX Mm + QM + “ l J}: I a ’ g (b) Find the first three nonzero terms of the series solution corresponding to the smaller root, if they differ by a non-integer. _ _ aH—i QVI m (5H,!) a0 _ C“ e- a” “1"” at: v [2 25' Q2 51.0 ...
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This note was uploaded on 01/10/2012 for the course MATH 2233 taught by Professor Binegar during the Fall '08 term at Oklahoma State.

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q13a - i/l S'WW QUIZZ 13 MATH 2233 SECTION 2, SPRING 2011...

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