What is the solution for xyy^'+x^2+y^2=0 ?

The solution for xyy^'+x^2+y^2=0 is y=(sqrt(-x^4+c_{1)})/(sqrt(2)x),y=-(sqrt(-x^4+c_{1)})/(sqrt(2)x)

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xyy^'+x^2+y^2=0

x y y^{^{'}} + x^{2} + y^{2} = 0

y = \frac{- x ^{4} + c _{1}}{2 x}, y = - \frac{- x ^{4} + c _{1}}{2 x}

Solution steps

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

Solve Bernoulli ODE:

y = \frac{- x ^{4} + c _{1}}{2 x}, y = - \frac{- x ^{4} + c _{1}}{2 x}

y = \frac{- x ^{4} + c _{1}}{2 x}, y = - \frac{- x ^{4} + c _{1}}{2 x}

\int \frac{5 x ^{4} + 6}{x ^{5} + 6 x} d x

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What is the solution for xyy^'+x^2+y^2=0 ?
The solution for xyy^'+x^2+y^2=0 is y=(sqrt(-x^4+c_{1)})/(sqrt(2)x),y=-(sqrt(-x^4+c_{1)})/(sqrt(2)x)