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

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

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

\frac{d y}{d x} = y - 2 y^{2}

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

Solution steps

\frac{d y}{d x} = y - 2 y^{2}

Solve separable ODE:

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

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

y^{^{'}} = \frac{6 y x ^{2}}{x ^{3} + 1}

y^{^{'}} = \frac{x}{y ^{2} 1 + x}

\frac{d y}{d x} = \frac{6 y}{x}, x > 0

y^{^{'}} = 3 \frac{y}{x - 1}

y^{^{'}} + 6 y = 4, y (0) = 0

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