What is the solution for (dx)/(dt)= 3/(xe^{t+7x)} ?

The solution for (dx)/(dt)= 3/(xe^{t+7x)} is x=(\W((-147e^{-t}+c_{1})/e))/(7)+1/7

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(dx)/(dt)= 3/(xe^{t+7x)}

\frac{d x}{d t} = \frac{3}{x e ^{t + 7 x}}

x = \frac{W ( \frac{- 147 e ^{- t} + c _{1}}{e} )}{7} + \frac{1}{7}

Solution steps

\frac{d x}{d t} = \frac{3}{x e ^{t + 7 x}}

Solve separable ODE:

x = \frac{W ( \frac{- 147 e ^{- t} + c _{1}}{e} )}{7} + \frac{1}{7}

x = \frac{W ( \frac{- 147 e ^{- t} + c _{1}}{e} )}{7} + \frac{1}{7}

y^{^{'}} sin (y) = cos (x), y (0) = 0

\frac{d x}{d t} + 1 = x

e^{y} (1 + x^{2}) \frac{d y}{d x} - 2 (1 + e^{y}) = 0

\frac{d y}{d x} = e^{x} y^{3}

y^{^{'}} = (5 x + 1) (y + 11), y (0) = 0

What is the solution for (dx)/(dt)= 3/(xe^{t+7x)} ?
The solution for (dx)/(dt)= 3/(xe^{t+7x)} is x=(\W((-147e^{-t}+c_{1})/e))/(7)+1/7