What is the solution for (dy)/(dx)=(1-y)/(1+e^x) ?

The solution for (dy)/(dx)=(1-y)/(1+e^x) is y=-e^{-x-c_{1}}-e^{-c_{1}}+1

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(dy)/(dx)=(1-y)/(1+e^x)

\frac{d y}{d x} = \frac{1 - y}{1 + e ^{x}}

y = - e^{- x - c_{1}} - e^{- c_{1}} + 1

Solution steps

\frac{d y}{d x} = \frac{1 - y}{1 + e ^{x}}

Solve separable ODE:

y = - e^{- x - c_{1}} - e^{- c_{1}} + 1

y = - e^{- x - c_{1}} - e^{- c_{1}} + 1

\frac{1}{2 x + 3}

x \to - 3 lim (x - 2)

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

y = 8 + 4 x^{2} - 2 x^{3}

6 (2 e^{x^{2}} x^{2} + e^{x^{2}})

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