If the seriesy(x)=

n=0

c

n

x

n

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

4xy

+3y=0

3y4xy+3y=0, thenc

n+2

=

cn+2=c

n

,n=0,1,2,...

cn,n=0,1,2,...

A general solution of the same equation can be written asy(x)=c

0

y

1

(x)+c

1

y

2

(x)

y(x)=c0y1(x)+c1y2(x)