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

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}