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

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

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

2 x y \frac{d y}{d x} + x^{2} + y^{2} = 0

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

Solution steps

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

\frac{d}{d x} (2 x^{2})

f (x) = 7 ln (3)

\int sec (x) \cdot tan^{2} (x) d x

\int_{l n (4)}^{l n (16)} e^{\frac{x}{2}} d x

3 x e^{- 2 x}

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