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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(dy)/(dx)=(2x)/(x+2)

\frac{d y}{d x} = \frac{2 x}{x + 2}

y = 2 (x + 2 - 2 ln (x + 2)) + c_{1}

Solution steps

\frac{d y}{d x} = \frac{2 x}{x + 2}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

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

then

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

y = \int \frac{2 x}{x + 2} d x

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

y = 2 (x + 2 - 2 ln (x + 2)) + c_{1}

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