What is the solution for (dy)/(dx)=y(1-y),y(0)=2 ?

The solution for (dy)/(dx)=y(1-y),y(0)=2 is y=-(2e^x)/(1-2e^x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)=y(1-y),y(0)=2

\frac{d y}{d x} = y (1 - y), y (0) = 2

y = - \frac{2 e ^{x}}{1 - 2 e ^{x}}

Solution steps

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

Solve separable ODE:

y = - \frac{2 e ^{x}}{1 - 2 e ^{x}}

y = - \frac{2 e ^{x}}{1 - 2 e ^{x}}

\frac{d}{d x} (\frac{- 2 x ^{2} + 2}{( 1 + x ^{2} ) ^{2}})

\frac{\partial}{\partial x} (- 4 y (- 2 x - y - 3))

\int 1 - \frac{16}{sin ^{4} ( x )} d x

x \to 0 lim (x ln^{2} (x))

\frac{\partial}{\partial x} (3 y^{2} - x^{2})

What is the solution for (dy)/(dx)=y(1-y),y(0)=2 ?
The solution for (dy)/(dx)=y(1-y),y(0)=2 is y=-(2e^x)/(1-2e^x)