What is the solution for (dx)/(dt)= 1/(xe^{t+5x)} ?

The solution for (dx)/(dt)= 1/(xe^{t+5x)} is x=(\W((-e^{-t}*25+c_{1})/e))/(5)+1/5

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(dx)/(dt)= 1/(xe^{t+5x)}

\frac{d x}{d t} = \frac{1}{x e ^{t + 5 x}}

x = \frac{W ( \frac{- e ^{- t} \cdot 25 + c _{1}}{e} )}{5} + \frac{1}{5}

Solution steps

\frac{d x}{d t} = \frac{1}{x e ^{t + 5 x}}

Solve separable ODE:

x = \frac{W ( \frac{- e ^{- t} \cdot 25 + c _{1}}{e} )}{5} + \frac{1}{5}

x = \frac{W ( \frac{- e ^{- t} \cdot 25 + c _{1}}{e} )}{5} + \frac{1}{5}

\int \frac{x ^{2}}{x ^{3} - 1} d x

\frac{\partial}{\partial x} (e^{- (x^{2} + x y + y^{2})})

(2 x y - 3) d x + (x^{2} + 4 y) d y = 0, y (1) = 2

\int 2 x^{2} x^{3} + 1 d x

x \to + 2 lim (\frac{2 x - 25}{x - 2})

What is the solution for (dx)/(dt)= 1/(xe^{t+5x)} ?
The solution for (dx)/(dt)= 1/(xe^{t+5x)} is x=(\W((-e^{-t}*25+c_{1})/e))/(5)+1/5