What is the solution for (dy)/(dx)=(2(y-1))/((x-1)) ?

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

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(dy)/(dx)=(2(y-1))/((x-1))

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d y}{d t} + 2 y = 0, y (0) = 3

\frac{d y}{d x} + 6 x^{2} y = 5 x^{2}, y (0) = 4

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

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

y^{^{'}} = \frac{2}{3} x 1 - 9 y^{2}, y (0) = 0

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