What is the solution for x^'=(1-x)(1-cos(pi)x) ?

The solution for x^'=(1-x)(1-cos(pi)x) 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)(1-cos(pi)x)

x^{^{'}} = (1 - x) (1 - cos (π) x)

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) (1 - cos (π) x)

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})}}

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