What is the solution for (dx)/(dt)= 5/(xe^{t+6x)} ?

The solution for (dx)/(dt)= 5/(xe^{t+6x)} is x=(\W((-180e^{-t}+c_{1})/e))/(6)+1/6

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(dx)/(dt)= 5/(xe^{t+6x)}

\frac{d x}{d t} = \frac{5}{x e ^{t + 6 x}}

x = \frac{W ( \frac{- 180 e ^{- t} + c _{1}}{e} )}{6} + \frac{1}{6}

Solution steps

\frac{d x}{d t} = \frac{5}{x e ^{t + 6 x}}

Solve separable ODE:

x = \frac{W ( \frac{- 180 e ^{- t} + c _{1}}{e} )}{6} + \frac{1}{6}

x = \frac{W ( \frac{- 180 e ^{- t} + c _{1}}{e} )}{6} + \frac{1}{6}

\int \frac{t}{2} d t

\frac{d}{d x} (x^{2} + 2 x + 1)

\int_{1}^{2} \int_{2}^{4} x y^{3} (e^{2})^{x^{2} y^{2}} d x d y

\int x cos (2 x) + x^{3} + 4 x + 2 + sec (2 x) d x

d x + d y \cdot e^{6 \cdot x} = 0

What is the solution for (dx)/(dt)= 5/(xe^{t+6x)} ?
The solution for (dx)/(dt)= 5/(xe^{t+6x)} is x=(\W((-180e^{-t}+c_{1})/e))/(6)+1/6