What is the solution for derivative of x^2+derivative of y^2=1 ?

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

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derivative of x^2+derivative of y^2=1

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

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} = \frac{1 + x}{x y}, y (1) = - 4

\frac{d y}{d x} + 4 x y = 4 e^{6} x

\frac{d v}{d t} = 0.4 v + 1000

\frac{d y}{y} = - \frac{d x}{x}

y^{^{'}} = \frac{4 \cdot y}{x} - \frac{4}{x}

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