What is the solution for xy^'=y^2-1 ?

The solution for xy^'=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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xy^'=y^2-1

x y^{^{'}} = 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 y^{'} (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}}

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