What is the solution for (dy)/(dx)=0.1y(1-y/(500)) ?

The solution for (dy)/(dx)=0.1y(1-y/(500)) is y=-(500e^{0.1x+c_{1}})/(1-e^{0.1x+c_{1)}}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)=0.1y(1-y/(500))

\frac{d y}{d x} = 0.1 y (1 - \frac{y}{500})

y = - \frac{500 e ^{0.1 x + c_{1}}}{1 - e ^{0.1 x + c_{1}}}

Solution steps

\frac{d y}{d x} = 0.1 y (1 - \frac{y}{500})

Solve separable ODE:

y = - \frac{500 e ^{0.1 x + c_{1}}}{1 - e ^{0.1 x + c_{1}}}

y = - \frac{500 e ^{0.1 x + c_{1}}}{1 - e ^{0.1 x + c_{1}}}

9 y^{^{''}} - 24 y^{^{'}} + 16 y = 0

y = \frac{1}{( x ^{2} - 2 ) ( x ^{2} + x + 5 )}

y = 5 x cos (x), (π, - 5 π)

y = csc^{3} (2 x)

\frac{d}{d x} ((a x + b) e^{- x})

What is the solution for (dy)/(dx)=0.1y(1-y/(500)) ?
The solution for (dy)/(dx)=0.1y(1-y/(500)) is y=-(500e^{0.1x+c_{1}})/(1-e^{0.1x+c_{1)}}