What is the solution for derivative of y^2=8x ?

The solution for derivative of y^2=8x is y=sqrt(4x^2+c_{1)},y=-sqrt(4x^2+c_{1)}

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derivative of y^2=8x

\frac{d}{d x} (y^{2}) = 8 x

y = 4 x^{2} + c_{1}, y = - 4 x^{2} + c_{1}

Solution steps

\frac{d}{d x} (y^{2}) = 8 x

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

then

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

y^{2} = \int 8 x d x

\int 8 x d x = 4 x^{2} + c_{1}

y^{2} = 4 x^{2} + c_{1}

Isolate

y : y = 4 x^{2} + c_{1}, y = - 4 x^{2} + c_{1}

y = 4 x^{2} + c_{1}, y = - 4 x^{2} + c_{1}

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

y^{^{'}} + 4 x y = 4 e^{6} x

\frac{d y}{d t} = - 0.7654 y

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

y^{5} \frac{d y}{d x} = 5 x^{3} y^{6} - 15 x^{3}

What is the solution for derivative of y^2=8x ?
The solution for derivative of y^2=8x is y=sqrt(4x^2+c_{1)},y=-sqrt(4x^2+c_{1)}