What is the solution for (dy)/(dt)=ln(5t-4) ?

The solution for (dy)/(dt)=ln(5t-4) is y=tln(5t-4)-4/5 ln(5t-4)-t+4/5+c_{1}

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

\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}

Solution steps

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

Substitute

\frac{d y}{d t}

with

y^{'} (t)

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

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

then

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}

What is the solution for (dy)/(dt)=ln(5t-4) ?
The solution for (dy)/(dt)=ln(5t-4) is y=tln(5t-4)-4/5 ln(5t-4)-t+4/5+c_{1}