What is the solution for (dy)/(dx)= x/(1+x^2) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)= x/(1+x^2)

\frac{d y}{d x} = \frac{x}{1 + x ^{2}}

y = \frac{1}{2} ln (1 + x^{2}) + c_{1}

Solution steps

\frac{d y}{d x} = \frac{x}{1 + x ^{2}}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{x}{1 + x ^{2}}

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

then

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

y = \int \frac{x}{1 + x ^{2}} d x

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

y = \frac{1}{2} ln (1 + x^{2}) + c_{1}

\frac{1}{3} y (y - 3)

x \to 1 lim (x^{2} - 2 x + 2)

\int (cos (t) sin (t)) d t

\frac{4 x}{( x ^{2} + 1 )}

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