Question

Iy yry 0, zo = 1

1-find the recurrence relation using power series solutions.
2-find the first four terms in each of two solutions y1 and y2
3-by evaluating wronskian w(y1,y2) show that they from a fundamental solution set.

Answer 1

Jy = o. 1. no nin- , (h-)n-2 G ( gn) ninc. n2 nn-), CH-1n1 + n n o <nC-"-' Cd1-1+)) E Cn (1-1)"z o di-1+1)Sn(n-1) c, (h-1)n-1 n n2 nc (-n- ni 2 n(n) C H-)"i + £ncn-1)C. (g1-1)"-a n 2 + n2 Co こ Cnldi-n+ + じ(-4)つて hao nニ0 (-4) u0+)3 + 20+2) (ntic。(カーon +SM+) C。(H-n ho naj nEo Co Cっ u n Cn+)C + (h+2)Cn+) ntDr 2+u- CnC + Cn + 2 C. + C, + identiua Gkich is equasiun.then Cm Rave

-'t Cn n+ + GN+1)( n+2) Cn+,+ LCn Cn-, Cn) C a (n+1) (n+a ) 3e4agenie &edn. たこhie seqised now ( 3)2 C4 3 C6+ 30

300 + 3G, 2 9 - Co Ch-1)° C, Ch1) + (, Gh-1 ) りもll-p)十 ()3 Li-リ3 1 2 (h1)2 _ 12 (H-)4 ti-1)

now こ キ thus and Rnie fundamunta