What is the solution for (dy}{dx}=\frac{y^2+2y)/2 ?

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

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(dy}{dx}=\frac{y^2+2y)/2

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

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} = 10 x^{3} y^{7}

9 t^{3} \frac{d x}{d t} + 6 x - 6 = 0

4 e d y - (y - 1)^{2} d x = 0

9 x^{3} y^{2} \frac{d y}{d x} = - 9 x^{2} y^{3}

\frac{d y}{d x} = \frac{cot ( x )}{y}, y (\frac{π}{2}) = 0

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