What is the solution for (dy)/(dx)=(1-y)(2-y) ?

The solution for (dy)/(dx)=(1-y)(2-y) is y=-(e^{x+c_{1}})/(1-e^{x+c_{1)}}+2/(1-e^{x+c_{1)}}

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(dy)/(dx)=(1-y)(2-y)

\frac{d y}{d x} = (1 - y) (2 - y)

y = - \frac{e ^{x + c_{1}}}{1 - e ^{x + c_{1}}} + \frac{2}{1 - e ^{x + c_{1}}}

Solution steps

\frac{d y}{d x} = (1 - y) (2 - y)

Solve separable ODE:

y = - \frac{e ^{x + c_{1}}}{1 - e ^{x + c_{1}}} + \frac{2}{1 - e ^{x + c_{1}}}

y = - \frac{e ^{x + c_{1}}}{1 - e ^{x + c_{1}}} + \frac{2}{1 - e ^{x + c_{1}}}

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