What is the solution for (dx)/(dt)= 4/(xe^{t+6x)} ?

The solution for (dx)/(dt)= 4/(xe^{t+6x)} is x=(\W((-144e^{-t}+c_{1})/e))/(6)+1/6

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(dx)/(dt)= 4/(xe^{t+6x)}

\frac{d x}{d t} = \frac{4}{x e ^{t + 6 x}}

x = \frac{W ( \frac{- 144 e ^{- t} + c _{1}}{e} )}{6} + \frac{1}{6}

Solution steps

\frac{d x}{d t} = \frac{4}{x e ^{t + 6 x}}

Solve separable ODE:

x = \frac{W ( \frac{- 144 e ^{- t} + c _{1}}{e} )}{6} + \frac{1}{6}

x = \frac{W ( \frac{- 144 e ^{- t} + c _{1}}{e} )}{6} + \frac{1}{6}

y^{^{'}} = \frac{( 3 x ^{2} )}{2 y}

\frac{d}{d x} (4 x^{3} + 2 y^{5}) = 6

\frac{d y}{d x} = (x - 1) (y + 1)

t^{2} y + 11 t y^{^{'}} - 11 y = 0, y^{1} (0) = t

\frac{d P}{d t} = 2 P - \frac{P ^{2}}{2}

What is the solution for (dx)/(dt)= 4/(xe^{t+6x)} ?
The solution for (dx)/(dt)= 4/(xe^{t+6x)} is x=(\W((-144e^{-t}+c_{1})/e))/(6)+1/6