What is the solution for (dp)/(dt)=6p(14-ln(p)) ?

The solution for (dp)/(dt)=6p(14-ln(p)) is p=e^{-e^{-6t-c_{1}}+14}

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(dp)/(dt)=6p(14-ln(p))

\frac{d p}{d t} = 6 p (14 - ln (p))

p = e^{- e^{- 6 t - c_{1}} + 14}

Solution steps

\frac{d p}{d t} = 6 p (14 - ln (p))

Solve separable ODE:

p = e^{- e^{- 6 t - c_{1}} + 14}

p = e^{- e^{- 6 t - c_{1}} + 14}

\frac{x d y}{d x} = y^{2}

2 (\frac{d q}{d t}) + 6 q = 2

\frac{2 x}{a ^{2}} + \frac{2 y \frac{d y}{d x}}{b ^{2}} = 0

\frac{d y}{d x} = - \frac{2 x}{3 y}

\frac{d y}{d x} = \frac{sin ( x )}{3 y}

What is the solution for (dp)/(dt)=6p(14-ln(p)) ?
The solution for (dp)/(dt)=6p(14-ln(p)) is p=e^{-e^{-6t-c_{1}}+14}