What is the solution for derivative of x^2+y^2= derivative of 9 ?

The solution for derivative of x^2+y^2= derivative of 9 is y=sqrt(-x^2+c_{1)},y=-sqrt(-x^2+c_{1)}

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derivative of x^2+y^2= derivative of 9

\frac{d}{d x} (x^{2} + y^{2}) = \frac{d}{d x} (9)

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

Solution steps

\frac{d}{d x} (x^{2} + y^{2}) = \frac{d}{d x} (9)

Solve separable ODE:

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

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

\frac{d y}{d x} = y, y (1) = 1

y = e^{\frac{3}{2 x}} \frac{d y}{d x}

e^{x} (x + 1) y^{2} d x + 2 x e^{x} y^{1} d y = 0

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

3 (2 + x^{2}) \frac{d y}{d x} = 2 x y (y^{3} - 1)

What is the solution for derivative of x^2+y^2= derivative of 9 ?
The solution for derivative of x^2+y^2= derivative of 9 is y=sqrt(-x^2+c_{1)},y=-sqrt(-x^2+c_{1)}