If you mean 6y"-7y'+y=0, or 6D2y-7Dy+y=0
6y"-7y'+y=0; solve 6r2-7r+1=(6r-1)(r-1)=0, so r=1 or ⅙.
This leads to y=Aex/6+Bex, where A and B are constants.
CHECK:
y'=Aex/6/6+Bex, y"=Aex/6/36+Bex.
6y"-7y'+y=Aex/6/6+6Bex-7Aex/6/6-7Bex+Aex/6+Bex=
Aex/6(⅙-7/6+1)+Bex(6-7+1)=0✔️