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

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

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(dy)/(dx)= y/(10)(500-y)

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

y = \frac{50}{e ^{- 50 x - c_{1}} - 1}

Solution steps

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

Solve Bernoulli ODE:

y = \frac{50}{e ^{- 50 x - c_{1}} - 1}

y = \frac{50}{e ^{- 50 x - c_{1}} - 1}

\frac{\partial}{\partial x} (- sin (x^{2} y) \cdot 2 x y)

\int \frac{x}{1 + 4 x ^{2}} d x

\frac{d}{d x} (\frac{x ^{2}}{2 x + 3})

\int_{0}^{1} \frac{65}{x ^{5}} d x

y^{^{'}} + 4 x y = 0

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