What is the solution for (dy)/(dx)=(x^2-xy-x+y)/(xy-y^2) ?

The solution for (dy)/(dx)=(x^2-xy-x+y)/(xy-y^2) is y=sqrt(-2x+x^2+c_{1)},y=-sqrt(-2x+x^2+c_{1)}

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(dy)/(dx)=(x^2-xy-x+y)/(xy-y^2)

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

y = - 2 x + x^{2} + c_{1}, y = - - 2 x + x^{2} + c_{1}

Solution steps

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

Solve separable ODE:

y = - 2 x + x^{2} + c_{1}, y = - - 2 x + x^{2} + c_{1}

y = - 2 x + x^{2} + c_{1}, y = - - 2 x + x^{2} + c_{1}

\frac{d y}{d x} = \frac{1 + y ^{2}}{x}

x^{2} (y^{2} + 1) d x + y x^{3} + 1 d y = 0

1 - x^{2} y^{^{'}} = 1 - y^{2}

y^{^{'}} = y (1 - \frac{y}{10})

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

What is the solution for (dy)/(dx)=(x^2-xy-x+y)/(xy-y^2) ?
The solution for (dy)/(dx)=(x^2-xy-x+y)/(xy-y^2) is y=sqrt(-2x+x^2+c_{1)},y=-sqrt(-2x+x^2+c_{1)}