What is the solution for (dy)/(dx)=((x-1))/((y-1)) ?

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

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(dy)/(dx)=((x-1))/((y-1))

\frac{d y}{d x} = \frac{( x - 1 )}{( y - 1 )}

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

Solution steps

\frac{d y}{d x} = \frac{( x - 1 )}{( y - 1 )}

Solve separable ODE:

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

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

\int_{0}^{0.1} x arctan (4 x) d x

\frac{d y}{d t} = \frac{8 t y}{t ^{2} + 1}

y^{^{'}} = 1 - t + y^{2} - t y^{2}

\frac{d}{d x} (- 7 sin (x))

\int \frac{d}{1} (x^{2} y) d x

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