What is the solution for y^'=0.05y(1-y/(4000)) ?

The solution for y^'=0.05y(1-y/(4000)) is y=-(4000e^{0.05t+c_{1}})/(1-e^{0.05t+c_{1)}}

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y^'=0.05y(1-y/(4000))

y^{^{'}} = 0.05 y (1 - \frac{y}{4000})

y = - \frac{4000 e ^{0.05 t + c_{1}}}{1 - e ^{0.05 t + c_{1}}}

Solution steps

y^{'} (t) = 0.05 y (1 - \frac{y}{4000})

Solve separable ODE:

y = - \frac{4000 e ^{0.05 t + c_{1}}}{1 - e ^{0.05 t + c_{1}}}

y = - \frac{4000 e ^{0.05 t + c_{1}}}{1 - e ^{0.05 t + c_{1}}}

- \frac{d h}{d t} = kh (t)^{n}

(x + \frac{x}{y}) d x - d y = 0

\frac{d y}{d x} y = sin^{3} (cos (9 x))

\frac{d y}{d t} 400 = - \frac{π}{9} \cdot 8 y

\frac{d y}{d x} = 85 y x^{16}, y = 4

What is the solution for y^'=0.05y(1-y/(4000)) ?
The solution for y^'=0.05y(1-y/(4000)) is y=-(4000e^{0.05t+c_{1}})/(1-e^{0.05t+c_{1)}}