What is the solution for (dx)/(dt)= 5/(xe^{t+8x)} ?

The solution for (dx)/(dt)= 5/(xe^{t+8x)} is x=(\W((-320e^{-t}+c_{1})/e))/(8)+1/8

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(dx)/(dt)= 5/(xe^{t+8x)}

\frac{d x}{d t} = \frac{5}{x e ^{t + 8 x}}

x = \frac{W ( \frac{- 320 e ^{- t} + c _{1}}{e} )}{8} + \frac{1}{8}

Solution steps

\frac{d x}{d t} = \frac{5}{x e ^{t + 8 x}}

Solve separable ODE:

x = \frac{W ( \frac{- 320 e ^{- t} + c _{1}}{e} )}{8} + \frac{1}{8}

x = \frac{W ( \frac{- 320 e ^{- t} + c _{1}}{e} )}{8} + \frac{1}{8}

\frac{d v}{d p} = \frac{- v}{p}

\frac{d y}{d x} - 0.2 x y = 0, y (1) = 1

\frac{d y}{d t} = 0.125 (y - 3), y (0) = 5

\frac{d y}{d x} = 2 y - 6

y y^{^{'}} = sin (x) + cos (x)

What is the solution for (dx)/(dt)= 5/(xe^{t+8x)} ?
The solution for (dx)/(dt)= 5/(xe^{t+8x)} is x=(\W((-320e^{-t}+c_{1})/e))/(8)+1/8