Question

DETAILS ZILLDIFFEQ9M 6.3.022. MY NOTES The point x = 0 is a regular singular point of the given differential equation. *?y" + xy' + +(x2-3) = 0 Show that the indicial roots r of the singularity do not differ by an integer. (List the indicial roots below as a comma-separated list.) Use the method of Frobenius to obtain two linearly independent series solutions about x = 0. Form the general solution on (0,co). 3 9 9 1 ...) 3328 448 5 25 25 + 32 3328 448 25 448 32 3328 5 25 25 448 3328 9 3 9 + 8 448 32 3328 O y = 0,*-*9(1 --) + cx/$(1 - 5x2 + 29**+. O y = C, x-313 (1 - 5 / -...) + C,x38(1 - ..) + Cyx35 /1 - 3 2 4 3 x² + + + + + +

Answer 1

0 + (22.2) - power { Countre senies solnton is OG © nzo & 2 (nere) (neret) en here te nere) enarr x²y" & myl Frubinuon Replace i put this in o =) Ź Mere) (nere -1) en antre nere tog mere) an a + no nzo & Ž GrH2+2 9 25 ě chunere nog nzo 3nd tenm n-2 in nao 720 nero f Ž Cn-2n -o 3 Ž cnnnere 25 n=2 nzo rel -) (recre-1)+re - 2 / 3 ) con + (8211) () +(241) - $)%* ŠTrening? - ) en a cn-2 + 12]* antre n=2 -Cn-2 cns - ) re2 q 5 (nerez) (nere + 3) Gro -3 3 5 ปก

-315 for r= 315 for ra C = -Cord Co-2 Cna n(n-08) n(n+) G= -Co -sco 8 2.45 32 2. 16 3 ay 11 493 Cya With 250 3328 4 szké 1 - :y(u) = C, X 5 R² 8 + 2507 448 + 25 24 & G 2351 - 14th ophon zs Connect 5u2 32 ---) 3328

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