Question

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

First order differential equations
ANSWERED
asked 2021-03-01

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

Answers (1)

2021-03-02

\(t^2 \frac{dy}{dt}+ty= 8 \ln^2t\)
\(\frac{dy}{(dt)}+\frac{y}{t}= \frac{8\ln^2t}{t^2}\)
\(I.F.= e^{\int \frac{1}{t} dt}= e^{\ln t}=t\)
\(yt= 8 \int \frac{\ln^2t}{t^2} tdt\)
\(yt= 8 \int \frac{\ln^2t}{t} dy\)
\(yt= \frac{8}{3} \ln^3(t)+c\)
\(y= \frac{8}{3t} \ln^3(t)+ \frac{c}{t}\)

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