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

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

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derivative of x^2+derivative of y^2=0

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

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} = \frac{4 y ^{2}}{x}

x^{^{'}} = - 5 x + 4 x

y \cdot y^{^{'}} - x \cdot y^{2} + x = 0

cos (2 y) d y = d x

y d x + (x - 1) d y = 0, y (2) = 25

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