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

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

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

y = ln (ln (1 + e^{x}) + c_{1})

Solution steps

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

Solve separable ODE:

y = ln (ln (1 + e^{x}) + c_{1})

y = ln (ln (1 + e^{x}) + c_{1})

\int \frac{x ^{2}}{( x ^{2} - 1 ) ^{\frac{3}{2}}} d x

f (x) = x^{2} - 5 x, at x = - 2

\int 9 x sin (x) cos (x) d x

f (x) = ∣ x ∣ 5 - x^{2}, (2, 2)

x \to 2 lim (3 x + 4 x)

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