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

The solution for (dy)/(dx)=e^x(1-y)^2 is y=-1/(e^x+c_{1)}+(e^x)/(e^x+c_{1)}+(c_{1})/(e^x+c_{1)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)=e^x(1-y)^2

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

y = - \frac{1}{e ^{x} + c _{1}} + \frac{e ^{x}}{e ^{x} + c _{1}} + \frac{c _{1}}{e ^{x} + c _{1}}

Solution steps

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

Solve separable ODE:

y = - \frac{1}{e ^{x} + c _{1}} + \frac{e ^{x}}{e ^{x} + c _{1}} + \frac{c _{1}}{e ^{x} + c _{1}}

y = - \frac{1}{e ^{x} + c _{1}} + \frac{e ^{x}}{e ^{x} + c _{1}} + \frac{c _{1}}{e ^{x} + c _{1}}

y^{^{'}} = sin (3 y)

\frac{d y}{d x} = e^{5 y} cos (\frac{x}{2})

(x^{2} - 3) \frac{d y}{d x} - x (y - 1) = 0

x + 3 y^{2} x^{2} + 1 \frac{d y}{d x} = 0

x^{2} y \frac{d y}{d x} + 2 x y^{2} = 0

What is the solution for (dy)/(dx)=e^x(1-y)^2 ?
The solution for (dy)/(dx)=e^x(1-y)^2 is y=-1/(e^x+c_{1)}+(e^x)/(e^x+c_{1)}+(c_{1})/(e^x+c_{1)}