What is the solution for (dx)/(dt)= 4/(xe^{t+3x)} ?

The solution for (dx)/(dt)= 4/(xe^{t+3x)} is x=(\W((-36e^{-t}+c_{1})/e))/(3)+1/3

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(dx)/(dt)= 4/(xe^{t+3x)}

\frac{d x}{d t} = \frac{4}{x e ^{t + 3 x}}

x = \frac{W ( \frac{- 36 e ^{- t} + c _{1}}{e} )}{3} + \frac{1}{3}

Solution steps

\frac{d x}{d t} = \frac{4}{x e ^{t + 3 x}}

Solve separable ODE:

x = \frac{W ( \frac{- 36 e ^{- t} + c _{1}}{e} )}{3} + \frac{1}{3}

x = \frac{W ( \frac{- 36 e ^{- t} + c _{1}}{e} )}{3} + \frac{1}{3}

- \frac{2 ( z ^{2} + 1 )}{z ^{2}}

\frac{d}{d t} (a t^{5} - 5 b t^{3})

\frac{\partial}{\partial x} (5 x y^{3})

\frac{d}{d x} ((\frac{x + 2}{x})^{3} + (\frac{x - 2}{x})^{3})

x^{4} + 3 x^{2} - x

What is the solution for (dx)/(dt)= 4/(xe^{t+3x)} ?
The solution for (dx)/(dt)= 4/(xe^{t+3x)} is x=(\W((-36e^{-t}+c_{1})/e))/(3)+1/3