What is the solution for derivative of x^2+y^2=0 ?

The solution for derivative of x^2+y^2=0 is y=sqrt(c_{1)-x^2},y=-sqrt(c_{1)-x^2}

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derivative of x^2+y^2=0

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

y = c_{1} - x^{2}, y = - c_{1} - x^{2}

Solution steps

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

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

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

\int 0 d x = c_{1}

x^{2} + y^{2} = c_{1}

Isolate

y : y = c_{1} - x^{2}, y = - c_{1} - x^{2}

y = c_{1} - x^{2}, y = - c_{1} - x^{2}

(8 + x) y^{^{'}} = (x + 9) (y - 8)

y^{2} d x - x y d y = x^{2} y d y, y (1) = 1

\frac{d y}{d x} = x (1 + y^{2}), y (0) = 0

\frac{d y}{d x} 5 x + 7 y + 6 = 0

y^{^{'}} = 1 + x + y^{2} + x y^{2}, y (0) = 1

What is the solution for derivative of x^2+y^2=0 ?
The solution for derivative of x^2+y^2=0 is y=sqrt(c_{1)-x^2},y=-sqrt(c_{1)-x^2}