What is the solution for xdy+sqrt(1+y^2)dx=0 ?

The solution for xdy+sqrt(1+y^2)dx=0 is y=-x/(2e^{c_{1)}}+(e^{c_{1}})/(2x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

xdy+sqrt(1+y^2)dx=0

x d y + 1 + y^{2} d x = 0

y = - \frac{x}{2 e ^{c_{1}}} + \frac{e ^{c_{1}}}{2 x}

Solution steps

x d y + 1 + y^{2} d x = 0

Solve separable ODE:

y = - \frac{x}{2 e ^{c_{1}}} + \frac{e ^{c_{1}}}{2 x}

y = - \frac{x}{2 e ^{c_{1}}} + \frac{e ^{c_{1}}}{2 x}

\frac{d y}{d x} + x y = \frac{x}{y ^{2}}, y (1) = 0.5

\frac{1}{x} \frac{d y}{d x} + 4 y = 2

(3 x + 8) (y^{2} + 4) d x - 4 y (x^{2} + 5 x + 6) d y = 0

\frac{d y}{d x} = \frac{y ln ( x )}{x}

y^{^{'}} = x y^{3} (1 + x^{2})^{- \frac{1}{2}}, y (0) = 1

What is the solution for xdy+sqrt(1+y^2)dx=0 ?
The solution for xdy+sqrt(1+y^2)dx=0 is y=-x/(2e^{c_{1)}}+(e^{c_{1}})/(2x)