Let [tex]y=x^r[/tex], then
[tex]x^2(r(r-1)x^{r-2})+4x(rx^{r-1})+2x^r=0[/tex]
[tex]r(r-1)x^r+4rx^r+2x^r=0[/tex]
[tex]r(r-1)+4r+2=0[/tex]
[tex]r^2+3r+2=0[/tex]
[tex](r+2)(r+1)=0[/tex]
[tex]r=-1,-2[/tex]
This admits a general solution of
[tex]y=C_1x^{-1}+C_2x^{-2}[/tex]
