f5df81cd-9a9d-4cb5-9269-1ba418f71739 6 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

2 x 2^* 1 x + 2 x 2^* + (* x y'' * x 911 x * + 11 x 2^* + (* x y' * + 610 x * + 7 x 2^* + (x y * + 0 ≡

x P 2 x 2^* 1 x + 2 x 2^* + (* :

x Q x 911 x * + 11 x 2^* + (* :

x R 610 x * + 7 x 2^* + (:

x Φ1 x x Q x P / * :

x Φ2 x 2^x R x P / * :

p0 x Φ1 x 0 lim :

q0 x Φ2 x 0 lim :

0 Φ1 0 Φ2 21 mat 4.5 321 mat

p0 4.5 :

q0 3 :

r r 1 - (* p0 r * + q0 + 0 ≡

r r 1 - (* p0 r * + q0 + r r 1 - (* 92 / r * + 3 + ≡

r r r 1 - (* p0 r * + q0 + r solve maple : 2 - 32 / - 21 mat

r indicial r r 1 - (* p0 r * + q0 + :

n 9 :

x indicial 0 2 - 0.05 2 - 0.05 - 2 2 mat 1.5 - 0.05 1.5 - 0.05 - 2 2 mat 4 1 sys

The Frobenius DE solutions

C1 113 / - 720 / - 928 / 1991440 / - 1032464 / - 21503174720 / 1192271597927 / - 3358867939763 / - 19 mat transpose :

x Y1 x r 1 el^C1 k el x k 1 -^* (k 1 n sum * :

C2 113 / - 12645 / - 1160 / 19225 / 1871080 / - 729181900 / 135120800 / 19 mat transpose :

x Y2 x r 2 el^C2 k el x k 1 -^* (k 1 n sum * :

The two Frobenius solutions

x Y1 x Y2 2 1 sys

This document illustrates the Frobenius method. The size of the expansion 'n' is "user". Smath Horner expansion doesn't enable the collocation of the 'C'. C1, C2 coefficients borrowed from Mathcad.