Question

8.6.24 Question Help Use the method of Frobenius and the larger indicial root to find the first four nonzero terms in the series expansion about x = 0 for a solution to the given equation for x>0. 3xy"' +(2-x)y' -y=0 What are the first four terms for the series? y(x) = + ... (Type an expression in terms of a..)

DIFFERENTIAL EQUATIONS / Linear Algebra

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Answer 1

3.6.24) 3xy" +(2-2) g'_y -Y 500 Let nto y I ana no => yl ntr- = E (nto) (1+r) and n=o 84 8W 11 => y" ntr-2 (1+r) (ntr-1 an de U MEO E 3(n+r) Intr-) an ntr- x + so ntrol 2 (n+r) an x nuo E 8W ner e ntry ana Игр E ntr ana. So Оси ntr A x S I 3 intr-) (n+r) anti + 2 intr+1) nan n=-1 ner 20 ner ntr anti į (1+r) anx .& 94 =0 WED neo 313 r18+)+Qr) a ६ 8-1 0C E [ B3 (n+r) -([n+r) +)an] Иe 0 in +r+1) +2 IntrH)] anti nto " O 38²-30728=0,

( 3(n+r) (n+r+i) +2 Intr+i)) ante intrti) an =0,tus, o =) 3r?-v=0 =) r(384) = = v=o, ya (n+rH) an anti OVA (n+r+) ( 3(n+) +2) the largest Toot r=1 / 3 = dosti an itnyo 3 Inti) loru ao 3 nal, a a 3.2 do Teen 18 93 az ao 3.3 S 00 9x18 .. 162 Hence 투 -) 410) = the solution 9(x) = (2018,x taxx++- Ja xål + + x 1.**...) 13.yu) H. (1++* * to listen ) tt x² 18 162 x = (W6( to