What is the solution for (dy)/(dx)=2-(2x)/(1000-x) ?

The solution for (dy)/(dx)=2-(2x)/(1000-x) is y=4x+2000ln(-x+1000)-2000+c_{1}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(dy)/(dx)=2-(2x)/(1000-x)

\frac{d y}{d x} = 2 - \frac{2 x}{1000 - x}

y = 4 x + 2000 ln (- x + 1000) - 2000 + c_{1}

Solution steps

\frac{d y}{d x} = 2 - \frac{2 x}{1000 - x}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 2 - \frac{2 x}{1000 - x}

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

then

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

y = \int 2 - \frac{2 x}{1000 - x} d x

\int 2 - \frac{2 x}{1000 - x} d x = 4 x + 2000 ln (- x + 1000) - 2000 + c_{1}

y = 4 x + 2000 ln (- x + 1000) - 2000 + c_{1}

What is the solution for (dy)/(dx)=2-(2x)/(1000-x) ?
The solution for (dy)/(dx)=2-(2x)/(1000-x) is y=4x+2000ln(-x+1000)-2000+c_{1}