What is the solution for (dy)/(dx)=((yx+3x-y-3))/(xy-2x+4y-8) ?

The solution for (dy)/(dx)=((yx+3x-y-3))/(xy-2x+4y-8) is y=-5\W(-(x+4}{5e^{\frac{x+c_{1}+3)/5}})-3

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(dy)/(dx)=((yx+3x-y-3))/(xy-2x+4y-8)

\frac{d y}{d x} = \frac{( y x + 3 x - y - 3 )}{x y - 2 x + 4 y - 8}

y = - 5 W (- \frac{x + 4}{5 e ^{\frac{x + c _{1} + 3}{5}}}) - 3

Solution steps

\frac{d y}{d x} = \frac{( y x + 3 x - y - 3 )}{x y - 2 x + 4 y - 8}

Solve separable ODE:

y = - 5 W (- \frac{x + 4}{5 e ^{\frac{x + c _{1} + 3}{5}}}) - 3

y = - 5 W (- \frac{x + 4}{5 e ^{\frac{x + c _{1} + 3}{5}}}) - 3

y^{^{'}} = e^{- y} + 1

x^{3} y d x + x^{2} y^{2} d y = 0

\frac{d y}{d x} = 2 x y^{2} + \frac{5 y ^{2}}{x}

\frac{d y}{d x} y = ln (ln (x^{5}))

y^{^{'}} = - 3 x^{2} (y + 2), y (1) = - 1

What is the solution for (dy)/(dx)=((yx+3x-y-3))/(xy-2x+4y-8) ?
The solution for (dy)/(dx)=((yx+3x-y-3))/(xy-2x+4y-8) is y=-5\W(-(x+4}{5e^{\frac{x+c_{1}+3)/5}})-3