What is the solution for 2sqrt(xy)((dy)/(dx))=3 ?

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

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2sqrt(xy)((dy)/(dx))=3

2 x y (\frac{d y}{d x}) = 3

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

Solution steps

2 x y (\frac{d y}{d 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}

\frac{d y}{d x} = 5 x (y + 4)^{3}

\frac{d y}{d x} 2 x^{3} = 2 y^{2} + 5

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

y^{^{'}} = a y + b, y (0) = c

\frac{d y}{d t} = - \frac{y}{100}

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