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

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

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(x^2+y^2)dx+2xydy=0

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

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

Solution steps

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