(dy)/(dt)=ln(5t-4)

解

\frac{d y}{d t} = ln (5 t - 4)

y = t ln (5 t - 4) - \frac{4}{5} ln (5 t - 4) - t + \frac{4}{5} + c_{1}

解答ステップ

\frac{d y}{d t} = ln (5 t - 4)

代用

\frac{d y}{d t}

と

y^{'} (t)

y^{^{'}} (t) = ln (5 t - 4)

f^{^{'}} (x) = g (x)

であれば

f (x) = \int g (x) d x

y = \int ln (5 t - 4) d t

\int ln (5 t - 4) d t = t ln (5 t - 4) - \frac{4}{5} ln (5 t - 4) - t + \frac{4}{5} + c_{1}

y = t ln (5 t - 4) - \frac{4}{5} ln (5 t - 4) - t + \frac{4}{5} + c_{1}