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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

(x^{2} + 37) y^{^{'}} = x y

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

y^{^{'}} = \frac{x}{y + x ^{2} y}, y (0) = - 2

\frac{d y}{d x} - y = 6, y = 2, x = 0

31 e^{x - 2 y} = 3 \frac{d x}{d y}

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