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

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

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

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

y = \frac{e ^{x + c_{1}}}{1 - e ^{x + c_{1}}} + \frac{1}{1 - e ^{x + c_{1}}}

Solution steps

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

Solve separable ODE:

y = \frac{e ^{x + c_{1}}}{1 - e ^{x + c_{1}}} + \frac{1}{1 - e ^{x + c_{1}}}

y = \frac{e ^{x + c_{1}}}{1 - e ^{x + c_{1}}} + \frac{1}{1 - e ^{x + c_{1}}}

y^{^{'}} = 6 x y - 3 y

y^{^{'}} = x y^{\frac{3}{2}}

y^{^{'}} = \frac{x}{2 y}

x \frac{d y}{d x} = e^{9 y + x}, x > 0

(1 + y^{2}) cos (x) d x - \frac{1}{x} d y = 0, y (0) = \frac{π}{4}

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