Question

1 point)

If the series y(x)=∑n=0∞cnxny(x)=∑n=0∞cnxn is a solution of the differential equation 1y″−6x2y′+2y=01y″−6x2y′+2y=0, then cn+2=cn+2=  cn−1+cn−1+  cn,n=1,2,…cn,n=1,2,…

A general solution of the same equation can be written as y(x)=c0y1(x)+c1y2(x)y(x)=c0y1(x)+c1y2(x), where

y1(x)=1+∑n=2∞anxn,y1(x)=1+∑n=2∞anxn,

y2(x)=x+∑n=2∞bnxn,y2(x)=x+∑n=2∞bnxn,

Calculate

a2=a2=  ,

a3=a3=  ,

a4=a4=  ,

b2=b2=  ,

b3=b3=  ,

b4=b4=  .

Answer 1