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

The solution for (y-x)e^x+(1+e^x)(dy)/(dx)=0 is y=(c_{1})/(1+e^x)+(e^xx)/(1+e^x)-(e^x)/(1+e^x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(y-x)e^x+(1+e^x)(dy)/(dx)=0

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

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

Solution steps

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

Solve exact ODE:

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

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

\int_{0}^{1} 2 π x (x - x) d x

\int_{1}^{7} (6 x^{2} + 2 x - 3) d x

n = 10 \sum \infty \frac{2}{3} (\frac{3}{4})^{n}

\int (1 + x)^{8} d x

t an g e n t \frac{7 x}{x - 1}

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