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

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

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

\frac{d y}{d x} = \frac{1 + y}{x - 1}

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

Solution steps

\frac{d y}{d x} = \frac{1 + y}{x - 1}

Solve separable ODE:

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

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

\frac{df}{d x} - x f (x) = 0

(2 x y^{4} + 2 x y^{2}) d x + (x^{2} y^{3} + x^{2} y) d y = 0

(1 + y^{2}) d x = (y - 1 + y^{2}) (1 + x^{2})^{\frac{3}{2}} d y

\frac{d y}{d t} = 5 + 5 y + t + t y, y (0) = 3

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

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