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

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

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

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

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

Solution steps

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

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^{^{'}} + 5 y = 20

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

y^{^{'}} - \frac{x}{5 y ^{4}} = 0

\frac{d y}{d x} = \frac{cos ^{2} ( x )}{y}

x d y - 2 y d x = 0

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