zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的微积分 >

x^'=e^{-x}+1

解答

x^{^{'}} = e^{- x} + 1

解答

x = ln (e^{t - c_{1}} - 1)

求解步骤

x^{'} (t) = e^{- x} + 1

求解

t, x^{'} (t) = \frac{d x}{d t} = \frac{1}{\frac{d t}{d x}} = \frac{1}{t ^{^{'}}}

(\frac{1}{t ^{^{^{'}}}}) = e^{- x} + 1

整理

t^{^{'}} : t^{^{'}} = \frac{e ^{x}}{1 + e ^{x}}

若

f^{^{'}} (x) = g (x)

则

f (x) = \int g (x) d x

t = \int \frac{e ^{x}}{1 + e ^{x}} d x

\int \frac{e ^{x}}{1 + e ^{x}} d x = ln (1 + e^{x}) + c_{1}

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

整理

x : x = ln (e^{t - c_{1}} - 1)

x = ln (e^{t - c_{1}} - 1)

作图

流行的例子

(dy)/(dx)y=(6+sin(x))^x

\frac{d y}{d x} y = (6 + sin (x))^{x}

\frac{d y}{d x} = k \cdot y

(1 + y) d y = y d x

x^'+3/200 x=0.06

x^{^{'}} + \frac{3}{200} x = 0.06

(dy)/(dx)-xy=xy^3

\frac{d y}{d x} - x y = x y^{3}