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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

y = c_{1} 1 + x^{2}

Solution steps

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

Solve separable ODE:

y = c_{1} 1 + x^{2}

y = c_{1} 1 + x^{2}

(e^{y} + 1) cos (x) d x + e^{y} sin (x) d y = 0

y \cdot e^{- x} d x - e^{- x} d y = 0

\frac{d y}{d x} - 2 y = 6

tan (x) sin^{3} (y) d x + sec^{3} (x) cos (y) d y = 0

y^{^{'}} csc (t) = - \frac{y ^{3}}{2}

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