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

The solution for (dx)/(dt)=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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(dx)/(dt)=1-x^2

\frac{d x}{d t} = 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

\frac{d x}{d 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})}}

\frac{d}{d x} (\frac{3 ( x ^{2} + 2 ) ^{3}}{5})

\frac{d x}{d t} = a x

\frac{( x + 1 )}{( x ^{2} + x + 1 )}

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

\frac{\partial}{\partial a} (a x)

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