\(t^2 dy/(dt)+ty= 8ln^2t\)

\(dy/(dt)+y/t= (8ln^2t)/t^2\)

\(I.F.= e^(int 1/t dt)= e^(ln t)=t\)

\(yt= 8 int (ln^2t)/t^2 tdt\)

\(yt= 8 int (ln^2t)/t dy\)

\(yt= 8/3 ln^3(t)+c\)

\(y= 8/(3t) ln^3(t)+ c/t\)

\(dy/(dt)+y/t= (8ln^2t)/t^2\)

\(I.F.= e^(int 1/t dt)= e^(ln t)=t\)

\(yt= 8 int (ln^2t)/t^2 tdt\)

\(yt= 8 int (ln^2t)/t dy\)

\(yt= 8/3 ln^3(t)+c\)

\(y= 8/(3t) ln^3(t)+ c/t\)