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})}}

\int 3 - 4 x^{2} d x

\int 12 cos (x) d x

\int \frac{x ^{3} - 9 x ^{2} - 1}{x ^{2} ( x + 1 ) ( x - 2 )} d x

\frac{\partial}{\partial x} (e^{\frac{x y}{z ^{2}}})

y^{^{''}} = \frac{2 k}{1 - k}

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))}}