What is the solution for (dx)/(dt)= 1/(xe^{t+3x)} ?

The solution for (dx)/(dt)= 1/(xe^{t+3x)} is x=(\W((-e^{-t}*9+c_{1})/e))/(3)+1/3

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(dx)/(dt)= 1/(xe^{t+3x)}

\frac{d x}{d t} = \frac{1}{x e ^{t + 3 x}}

x = \frac{W ( \frac{- e ^{- t} \cdot 9 + c _{1}}{e} )}{3} + \frac{1}{3}

Solution steps

\frac{d x}{d t} = \frac{1}{x e ^{t + 3 x}}

Solve separable ODE:

x = \frac{W ( \frac{- e ^{- t} \cdot 9 + c _{1}}{e} )}{3} + \frac{1}{3}

x = \frac{W ( \frac{- e ^{- t} \cdot 9 + c _{1}}{e} )}{3} + \frac{1}{3}

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What is the solution for (dx)/(dt)= 1/(xe^{t+3x)} ?
The solution for (dx)/(dt)= 1/(xe^{t+3x)} is x=(\W((-e^{-t}*9+c_{1})/e))/(3)+1/3