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

The solution for x^'=1-x^2 is x=-(e^{2t+2c_{1}})/(1-e^{2(t+c_{1))}}-1/(1-e^{2(t+c_{1))}}

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x^'=1-x^2

x^{^{'}} = 1 - x^{2}

x = - \frac{e ^{2 t + 2 c_{1}}}{1 - e ^{2 (t + c_{1})}} - \frac{1}{1 - e ^{2 (t + c_{1})}}

Solution steps

x^{'} (t) = 1 - x^{2}

Solve separable ODE:

x = - \frac{e ^{2 t + 2 c_{1}}}{1 - e ^{2 (t + c_{1})}} - \frac{1}{1 - e ^{2 (t + c_{1})}}

x = - \frac{e ^{2 t + 2 c_{1}}}{1 - e ^{2 (t + c_{1})}} - \frac{1}{1 - e ^{2 (t + c_{1})}}

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What is the solution for x^'=1-x^2 ?
The solution for x^'=1-x^2 is x=-(e^{2t+2c_{1}})/(1-e^{2(t+c_{1))}}-1/(1-e^{2(t+c_{1))}}