What is the solution for (dx)/(dt)= 1/(xe^{t+9x)} ?

The solution for (dx)/(dt)= 1/(xe^{t+9x)} is x=(\W((-e^{-t}*81+c_{1})/e))/(9)+1/9

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(dx)/(dt)= 1/(xe^{t+9x)}

\frac{d x}{d t} = \frac{1}{x e ^{t + 9 x}}

x = \frac{W ( \frac{- e ^{- t} \cdot 81 + c _{1}}{e} )}{9} + \frac{1}{9}

Solution steps

\frac{d x}{d t} = \frac{1}{x e ^{t + 9 x}}

Solve separable ODE:

x = \frac{W ( \frac{- e ^{- t} \cdot 81 + c _{1}}{e} )}{9} + \frac{1}{9}

x = \frac{W ( \frac{- e ^{- t} \cdot 81 + c _{1}}{e} )}{9} + \frac{1}{9}

\frac{d y}{d x} = \frac{x ^{5} y}{16 - x ^{6}}

y^{^{'}} = 0.0175 \cdot 7 - \frac{y}{2000} \cdot 7

y^{^{'}} = \frac{2 y ^{4} - 2}{( 4 x y ^{3} )}

a y - b y^{^{'}} = 0

\frac{d y}{d x} = 7 x + x y

What is the solution for (dx)/(dt)= 1/(xe^{t+9x)} ?
The solution for (dx)/(dt)= 1/(xe^{t+9x)} is x=(\W((-e^{-t}*81+c_{1})/e))/(9)+1/9