What is the solution for 2sqrt(xy)(y^')=3 ?

The solution for 2sqrt(xy)(y^')=3 is y=\sqrt[3]{(81x)/4+(27c_{1}sqrt(x))/2+(9c_{1}^2)/4}

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2sqrt(xy)(y^')=3

2 x y (y^{^{'}}) = 3

y = 3 \frac{81 x}{4} + \frac{27 c _{1} x}{2} + \frac{9 c _{1}^{2}}{4}

Solution steps

2 x y (y^{'} (x)) = 3

Solve separable ODE:

y = 3 \frac{81 x}{4} + \frac{27 c _{1} x}{2} + \frac{9 c _{1}^{2}}{4}

y = 3 \frac{81 x}{4} + \frac{27 c _{1} x}{2} + \frac{9 c _{1}^{2}}{4}

y^{^{'}} = e^{4 x - y}

(1 + y) \cdot d x + (\frac{d y}{( x ^{2} - 2 \cdot x )}) = 0

\frac{d y}{d t} = y^{2} - 9

\frac{d}{d x} (a x^{2} y) = \frac{d}{d x} (7)

\frac{4}{x} \frac{d y}{d x} = \frac{1}{y ^{3}}

What is the solution for 2sqrt(xy)(y^')=3 ?
The solution for 2sqrt(xy)(y^')=3 is y=\sqrt[3]{(81x)/4+(27c_{1}sqrt(x))/2+(9c_{1}^2)/4}