What is the solution for dy(xy-2x+4y-8)-dx(xy+3x-y-3)=0 ?

The solution for dy(xy-2x+4y-8)-dx(xy+3x-y-3)=0 is y=-5\W(-(x+4}{5e^{\frac{x+c_{1}+3)/5}})-3

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dy(xy-2x+4y-8)-dx(xy+3x-y-3)=0

d y (x y - 2 x + 4 y - 8) - d x (x y + 3 x - y - 3) = 0

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

Solution steps

d y (x y - 2 x + 4 y - 8) - d x (x y + 3 x - y - 3) = 0

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

(4 y - 5) d x + (7 x - 2) d y = 0

y^{^{'}} + y^{2} - y = 0

(6 y^{2} + 4 x y^{3}) d x + (6 x y + 4 x^{2} y^{2}) d y = 0

\frac{d y}{d x} = 600 y

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

What is the solution for dy(xy-2x+4y-8)-dx(xy+3x-y-3)=0 ?
The solution for dy(xy-2x+4y-8)-dx(xy+3x-y-3)=0 is y=-5\W(-(x+4}{5e^{\frac{x+c_{1}+3)/5}})-3