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

The solution for (dx)/(dt)= 3/(xe^{t+3x)} is x=(\W((-27e^{-t}+c_{1})/e))/(3)+1/3

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

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

x = \frac{W ( \frac{- 27 e ^{- t} + c _{1}}{e} )}{3} + \frac{1}{3}

Solution steps

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

Solve separable ODE:

x = \frac{W ( \frac{- 27 e ^{- t} + c _{1}}{e} )}{3} + \frac{1}{3}

x = \frac{W ( \frac{- 27 e ^{- t} + c _{1}}{e} )}{3} + \frac{1}{3}

What is the solution for (dx)/(dt)= 3/(xe^{t+3x)} ?
The solution for (dx)/(dt)= 3/(xe^{t+3x)} is x=(\W((-27e^{-t}+c_{1})/e))/(3)+1/3