What is the solution for (dy)/(dx)=0.1y(1-0.5y),y(0)=5000 ?

The solution for (dy)/(dx)=0.1y(1-0.5y),y(0)=5000 is y=-(5000e^{0.1x})/(2499-2500e^{0.1x)}

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(dy)/(dx)=0.1y(1-0.5y),y(0)=5000

\frac{d y}{d x} = 0.1 y (1 - 0.5 y), y (0) = 5000

y = - \frac{5000 e ^{0.1 x}}{2499 - 2500 e ^{0.1 x}}

Solution steps

\frac{d y}{d x} = 0.1 y (1 - 0.5 y)

Solve separable ODE:

y = - \frac{5000 e ^{0.1 x}}{2499 - 2500 e ^{0.1 x}}

y = - \frac{5000 e ^{0.1 x}}{2499 - 2500 e ^{0.1 x}}

\frac{d y}{d t} + 0.4 t y = 4 t

y^{^{'}} = (1 + 4 x) y

y^{^{'}} + 18 x y = 0

x^{^{'}} + a x = b

x^{^{'}} = 1 - 2.2 x

What is the solution for (dy)/(dx)=0.1y(1-0.5y),y(0)=5000 ?
The solution for (dy)/(dx)=0.1y(1-0.5y),y(0)=5000 is y=-(5000e^{0.1x})/(2499-2500e^{0.1x)}