What is the solution for (x\frac{dy)/(dx)-y}{xy}-1+7(dy)/(dx)=e^x ?

The solution for (x\frac{dy)/(dx)-y}{xy}-1+7(dy)/(dx)=e^x is y=(\W((x*7)/(e^{-e^x-x-c_{1)}}))/7

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(x\frac{dy)/(dx)-y}{xy}-1+7(dy)/(dx)=e^x

\frac{x \frac{d y}{d x} - y}{x y} - 1 + 7 \frac{d y}{d x} = e^{x}

y = \frac{W ( \frac{x \cdot 7}{e ^{- e^{x} - x - c_{1}}} )}{7}

Solution steps

\frac{x \frac{d y}{d x} - y}{x y} - 1 + 7 \frac{d y}{d x} = e^{x}

Solve separable ODE:

y = \frac{W ( \frac{x \cdot 7}{e ^{- e^{x} - x - c_{1}}} )}{7}

y = \frac{W ( \frac{x \cdot 7}{e ^{- e^{x} - x - c_{1}}} )}{7}

y^{^{'}} = y t, y (0) = 2

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

y^{^{'}} = n \frac{y}{x}

\frac{d x}{d t} = r - k x

\frac{d y}{d x} = 5 y, y (2) = 2

What is the solution for (x\frac{dy)/(dx)-y}{xy}-1+7(dy)/(dx)=e^x ?
The solution for (x\frac{dy)/(dx)-y}{xy}-1+7(dy)/(dx)=e^x is y=(\W((x*7)/(e^{-e^x-x-c_{1)}}))/7