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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d y}{d x} = - \frac{2 x}{6 y}

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

y^{^{'}} + y = y (sin (x) + 1)

\frac{d y}{d x} = 2 y tan (x)

(x^{2} + 1) sin (y) y^{^{'}} = - 2 x cos (y)

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