What is the solution for derivative of x^2+y^2= derivative of 16 ?

The solution for derivative of x^2+y^2= derivative of 16 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 16

\frac{d}{d x} (x^{2} + y^{2}) = \frac{d}{d x} (16)

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

Solution steps

\frac{d}{d x} (x^{2} + y^{2}) = \frac{d}{d x} (16)

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} = \frac{- 0.1}{cos ( y )}, y (0) = \frac{π}{3}

\frac{d y}{d x} = y (x^{2} + 5)

y^{^{'}} - 12 x y = 9 x

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

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

What is the solution for derivative of x^2+y^2= derivative of 16 ?
The solution for derivative of x^2+y^2= derivative of 16 is y=sqrt(-x^2+c_{1)},y=-sqrt(-x^2+c_{1)}