What is the solution for (dy)/(dt)=ay(1-y) ?

The solution for (dy)/(dt)=ay(1-y) is y=-(e^{at+c_{1}})/(1-e^{at+c_{1)}}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dt)=ay(1-y)

\frac{d y}{d t} = a y (1 - y)

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

Solution steps

\frac{d y}{d t} = a y (t) (1 - y)

Solve separable ODE:

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

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

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

(\frac{2 x}{y}) d y + (\frac{2 ln ( 5 y ) + 1}{x}) d x = 0

sin (t) cos (x) d t + sin (x) cos (t) d x = 0

\frac{d y}{d x} = e^{2 y}

x^{^{'}} = e^{- x}

What is the solution for (dy)/(dt)=ay(1-y) ?
The solution for (dy)/(dt)=ay(1-y) is y=-(e^{at+c_{1}})/(1-e^{at+c_{1)}}