# Solve differential equation t^2dy= (8ln^2t-ty)dt

Question
Solve differential equation $$t^2dy= (8ln^2t-ty)dt$$

2021-03-02
$$t^2 dy/(dt)+ty= 8ln^2t$$
$$dy/(dt)+y/t= (8ln^2t)/t^2$$
$$I.F.= e^(int 1/t dt)= e^(ln t)=t$$
$$yt= 8 int (ln^2t)/t^2 tdt$$
$$yt= 8 int (ln^2t)/t dy$$
$$yt= 8/3 ln^3(t)+c$$
$$y= 8/(3t) ln^3(t)+ c/t$$

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