What is the solution for (dx)/(dt)= 1/(xe^{t+2x)} ?

The solution for (dx)/(dt)= 1/(xe^{t+2x)} is x=(\W((-e^{-t}*4+c_{1})/e))/(2)+1/2

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(dx)/(dt)= 1/(xe^{t+2x)}

\frac{d x}{d t} = \frac{1}{x e ^{t + 2 x}}

x = \frac{W ( \frac{- e ^{- t} \cdot 4 + c _{1}}{e} )}{2} + \frac{1}{2}

Solution steps

\frac{d x}{d t} = \frac{1}{x e ^{t + 2 x}}

Solve separable ODE:

x = \frac{W ( \frac{- e ^{- t} \cdot 4 + c _{1}}{e} )}{2} + \frac{1}{2}

x = \frac{W ( \frac{- e ^{- t} \cdot 4 + c _{1}}{e} )}{2} + \frac{1}{2}

a \to 0 lim (ln (a))

n = 1 \sum \infty \frac{9 n ^{7}}{n !}

\frac{d x}{d t} = - (x^{2} - x), x (0) = 2

\int_{0}^{3} ∣ 2 x - 3 ∣ d x

y^{^{''}} - y^{^{'}} - 6 y = 0, y (0) = 2, y^{^{'}} (0) = 2

What is the solution for (dx)/(dt)= 1/(xe^{t+2x)} ?
The solution for (dx)/(dt)= 1/(xe^{t+2x)} is x=(\W((-e^{-t}*4+c_{1})/e))/(2)+1/2