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

The solution for (dy)/(dx)=(-y^2)/(1+y^2)e^{(-x)},y(0)=1 is y=(-e^x+1+sqrt(-2e^x+5e^{2x)+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^2)/(1+y^2)e^{(-x)},y(0)=1

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

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

Solution steps

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

Solve separable ODE:

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

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

\int \frac{x ^{2} - 5 x + 16}{x ( x - 2 ) ^{2}} d x

y = 12 x, y = x^{2}

n = 0 \sum \infty (2)^{n}

\frac{d}{d x} (\frac{x ^{3}}{3})

y^{^{''}} - 2 y^{^{'}} = 8 x + e^{x}

What is the solution for (dy)/(dx)=(-y^2)/(1+y^2)e^{(-x)},y(0)=1 ?
The solution for (dy)/(dx)=(-y^2)/(1+y^2)e^{(-x)},y(0)=1 is y=(-e^x+1+sqrt(-2e^x+5e^{2x)+1})/(2e^x)