What is the solution for derivative of sqrt(x)+sqrt(y)=1 ?

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

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derivative of sqrt(x)+sqrt(y)=1

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

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

Solution steps

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

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

then

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

x + y = \int 1 d x

\int 1 d x = x + c_{1}

x + y = x + c_{1}

Isolate

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

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

(1 + e^{x}) y \cdot y^{^{'}} = e^{y}

x y^{^{'}} - y = 0, y (0) = x

y^{^{'}} - y = 0, y (0) = 2

\frac{d y}{d t} = 0.04 - \frac{y}{( \frac{4320}{7} )}

y^{^{'}} = \frac{2 x y - 2 x}{x ^{2} + 3}

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