What is the solution for 7sqrt(xy)(dy)/(dx)=3 ?

The solution for 7sqrt(xy)(dy)/(dx)=3 is y=\sqrt[3]{(81x}{49}+\frac{27c_{1}sqrt(x))/7+(9c_{1}^2)/4}

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7sqrt(xy)(dy)/(dx)=3

7 x y \frac{d y}{d x} = 3

y = 3 \frac{81 x}{49} + \frac{27 c _{1} x}{7} + \frac{9 c _{1}^{2}}{4}

Solution steps

7 x y \frac{d y}{d x} = 3

Solve separable ODE:

y = 3 \frac{81 x}{49} + \frac{27 c _{1} x}{7} + \frac{9 c _{1}^{2}}{4}

y = 3 \frac{81 x}{49} + \frac{27 c _{1} x}{7} + \frac{9 c _{1}^{2}}{4}

x \frac{d y}{d x} = y + x y

y^{^{'}} = (\frac{2 y + 3}{4 t + 5})^{2}

x \frac{d y}{d x} = e^{y + x}, x > 0

y^{^{'}} - \frac{3 y}{x} = 0

(1 - x) y^{^{'}} = 6 y

What is the solution for 7sqrt(xy)(dy)/(dx)=3 ?
The solution for 7sqrt(xy)(dy)/(dx)=3 is y=\sqrt[3]{(81x}{49}+\frac{27c_{1}sqrt(x))/7+(9c_{1}^2)/4}