What is the solution for (dx)/(dt)= 3/(xe^{t+6x)} ?

The solution for (dx)/(dt)= 3/(xe^{t+6x)} is x=(\W((-108e^{-t}+c_{1})/e))/(6)+1/6

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(dx)/(dt)= 3/(xe^{t+6x)}

\frac{d x}{d t} = \frac{3}{x e ^{t + 6 x}}

x = \frac{W ( \frac{- 108 e ^{- t} + c _{1}}{e} )}{6} + \frac{1}{6}

Solution steps

\frac{d x}{d t} = \frac{3}{x e ^{t + 6 x}}

Solve separable ODE:

x = \frac{W ( \frac{- 108 e ^{- t} + c _{1}}{e} )}{6} + \frac{1}{6}

x = \frac{W ( \frac{- 108 e ^{- t} + c _{1}}{e} )}{6} + \frac{1}{6}

What is the solution for (dx)/(dt)= 3/(xe^{t+6x)} ?
The solution for (dx)/(dt)= 3/(xe^{t+6x)} is x=(\W((-108e^{-t}+c_{1})/e))/(6)+1/6