What is the solution for (dy)/(dx)= 1/10 (500y-y^2) ?

The solution for (dy)/(dx)= 1/10 (500y-y^2) is y=-(500e^{50x+50c_{1}})/(1-e^{50(x+c_{1))}}

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(dy)/(dx)= 1/10 (500y-y^2)

\frac{d y}{d x} = \frac{1}{10} (500 y - y^{2})

y = - \frac{500 e ^{50 x + 50 c_{1}}}{1 - e ^{50 (x + c_{1})}}

Solution steps

\frac{d y}{d x} = \frac{1}{10} (500 y - y^{2})

Solve separable ODE:

y = - \frac{500 e ^{50 x + 50 c_{1}}}{1 - e ^{50 (x + c_{1})}}

y = - \frac{500 e ^{50 x + 50 c_{1}}}{1 - e ^{50 (x + c_{1})}}

\frac{d y}{d t} = e^{- y}

\int \frac{1}{9} e^{9 x} d x

\frac{d}{d x} (\frac{6 x ^{2} + 1}{x ^{2} + 9})

\int \frac{y}{( y + 7 ) ( 2 y - 1 )} d y

- y^{^{''}} = 1

What is the solution for (dy)/(dx)= 1/10 (500y-y^2) ?
The solution for (dy)/(dx)= 1/10 (500y-y^2) is y=-(500e^{50x+50c_{1}})/(1-e^{50(x+c_{1))}}