Here is the question:

If the seriesy(x)=

n=0

c

n

x

n

y(x)=n=0cnxnis a solution of the differential equation3y

1xy=0

3y1xy=0, thenc

n+2

=

cn+2=c

n1

,n=1,2,...

W lfthe series y(.t] = E ux" is a solution ofthe differential equation 3)" lxy = D. then cm; = on"; , r1 = 1, 2, 11:0 A general solution of the same equation can be written as x) = cuyl (x) + any; (x). where m 3M1) = Ednx",u =1. 11:13 no MI) = Ebuxmhbu =1 \":0 Calculate is\" 3 II II o- ._. ll .5" II