Question

+ Use the Frobenius method to Cindd yCa ) and use the denvative method foc firdiny y2Ca), and plug in the Porm the solution 4o show what value the undetermined QBntantsyields the Same Solution as that afrived in +he deriuativepart

Answer 1

Questiom use the Fobuius Method to imd y, ( x) ond us Hhe omd plu9 deriva tive MiHhod for Jimdiniq he th lov d the Solution to Shois what alut d Constout Yidds the Some Solution detevmind os that Arvivd i thi derivative Part Amswev By usimg Frobenius Mithod: a) х?у +y -о: Qet ycx) Ytk S(k (v+k-1) ak ak+Y~ 1 -о* K-o K o E Crtk) (Yk- 1)aktak- YCY-) ao k k- O CS Scanned CamScanner

ond a K- O K |=人ニ人 (-1)ao Ck1)(k)2 ak- O K 2 ak (KH) K2Ck- ) Ck1)k CK) (K!)2 KEO CY,) (-1K kt kso (k+) k!)2 CS Scanned with CamScanner

(b) usima oerivative Mcthod: bexk CY, CxLn x)+x K-o Cx) Ln Cx)+ k o CY )xy" 2 cy,Cxy," Ln ) dx ko 2. y Y= o et y =) CL CY,Ln cx) 2Cy,- CY KEo - 2Cy Ko + C2b,+bx Sca C-C ) C20 bs tbu24 43 2 320 bo= -L 3 c 2 bb 2. cs Scanned with CamScanner 2 t 3

Av bi tray CoMstomt (s -bo CC Nos, bo vii on Notile b, Con also be choosu Arbi tarity this elleciunt it is the Co - i th Sevies K + K-o Jovan , C) dit bo ond bo b2 36 1- 2 35a4 3 X 3 6 28 CS Scanned with CamScanner