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

The solution for (dy)/(dx)=(x^2)/(x^2+1) is y=-arctan(x)+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)=(x^2)/(x^2+1)

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

y = - arctan (x) + x + c_{1}

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

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

then

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

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

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

y = - arctan (x) + x + c_{1}

\int 2 + 3 x - 4 y^{3} d x

\int_{0}^{9} π (2 3 y)^{2} d y

\frac{d}{d x} (x^{3} + 2 x - 5)

x \to 4 lim (\frac{2 x - 1}{x - 4})

\int 5 x e^{- x} d x

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