What is the solution for 2sqrt(xy)*(dy)/(dx)=1 ?

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

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2sqrt(xy)*(dy)/(dx)=1

2 x y \cdot \frac{d y}{d x} = 1

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

Solution steps

2 x y \cdot \frac{d y}{d x} = 1

Solve separable ODE:

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

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

y^{^{'}} = (1 + y^{2}) e^{x}

\frac{d y}{d x} = 4 + 12 x + 6 y + 18 x y

y^{^{'}} = x^{2} - 3 x^{2} y

\frac{d y}{d x} = \frac{2 y + 5}{- 5 x - 2}

\frac{d y}{d x} y = x^{2} + 8

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