What is the solution for derivative of xy^2=6 ?

The solution for derivative of xy^2=6 is y=sqrt(6+(c_{1))/x},y=-sqrt(6+(c_{1))/x}

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derivative of xy^2=6

\frac{d}{d x} (x y^{2}) = 6

y = 6 + \frac{c _{1}}{x}, y = - 6 + \frac{c _{1}}{x}

Solution steps

\frac{d}{d x} (x y^{2}) = 6

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

then

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

x y^{2} = \int 6 d x

\int 6 d x = 6 x + c_{1}

x y^{2} = 6 x + c_{1}

Isolate

y : y = 6 + \frac{c _{1}}{x}, y = - 6 + \frac{c _{1}}{x}

y = 6 + \frac{c _{1}}{x}, y = - 6 + \frac{c _{1}}{x}

y^{^{'}} + \frac{y}{5} = y^{- 3}

y^{^{'}} = e^{(x - 2 y)}

2 y y^{^{'}} = x e^{x}

f^{^{'}} (x) = \frac{1}{1 - ( f ( x ) ) ^{2}}, f (x) (g (x)) = x

y^{^{'}} = x e^{5 x - 3 y}, y (0) = 2

What is the solution for derivative of xy^2=6 ?
The solution for derivative of xy^2=6 is y=sqrt(6+(c_{1))/x},y=-sqrt(6+(c_{1))/x}