\(t^2 \frac{dy}{dt}+ty= 8 \ln^2t\)

\(\frac{dy}{(dt)}+\frac{y}{t}= \frac{8\ln^2t}{t^2}\)

\(I.F.= e^{\int \frac{1}{t} dt}= e^{\ln t}=t\)

\(yt= 8 \int \frac{\ln^2t}{t^2} tdt\)

\(yt= 8 \int \frac{\ln^2t}{t} dy\)

\(yt= \frac{8}{3} \ln^3(t)+c\)

\(y= \frac{8}{3t} \ln^3(t)+ \frac{c}{t}\)