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

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

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

Answers (1)

2021-03-02
\(t^2 dy/(dt)+ty= 8ln^2t\)
\(dy/(dt)+y/t= (8ln^2t)/t^2\)
\(I.F.= e^(int 1/t dt)= e^(ln t)=t\)
\(yt= 8 int (ln^2t)/t^2 tdt\)
\(yt= 8 int (ln^2t)/t dy\)
\(yt= 8/3 ln^3(t)+c\)
\(y= 8/(3t) ln^3(t)+ c/t\)
0

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