What is the solution for (2xy)dy+(x^2+y^2)dx=0 ?

The solution for (2xy)dy+(x^2+y^2)dx=0 is y=sqrt(-(x^2)/3+(c_{1))/x},y=-sqrt(-(x^2)/3+(c_{1))/x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(2xy)dy+(x^2+y^2)dx=0

(2 x y) d y + (x^{2} + y^{2}) d x = 0

y = - \frac{x ^{2}}{3} + \frac{c _{1}}{x}, y = - - \frac{x ^{2}}{3} + \frac{c _{1}}{x}

Solution steps

(2 x y) d y + (x^{2} + y^{2}) d x = 0

Solve Bernoulli ODE:

y = - \frac{x ^{2}}{3} + \frac{c _{1}}{x}, y = - - \frac{x ^{2}}{3} + \frac{c _{1}}{x}

y = - \frac{x ^{2}}{3} + \frac{c _{1}}{x}, y = - - \frac{x ^{2}}{3} + \frac{c _{1}}{x}

What is the solution for (2xy)dy+(x^2+y^2)dx=0 ?
The solution for (2xy)dy+(x^2+y^2)dx=0 is y=sqrt(-(x^2)/3+(c_{1))/x},y=-sqrt(-(x^2)/3+(c_{1))/x}