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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)=(2xy)/(x^2+1),y(1)=2

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

y = x^{2} + 1

Solution steps

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

Solve separable ODE:

y = x^{2} + 1

y = x^{2} + 1

x d x - y d y = x y (x d y - y d x)

\frac{d y}{d x} = \frac{sin ( x )}{sec ^{2} ( y )}

y^{^{'}} = \frac{y ^{4}}{x ^{6}}

\frac{d p}{d t} = p \cdot (1 - p \cdot 1 0^{- 4})

x y^{2} - 7 y^{2} - x^{2} y^{^{'}} = 0

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