What is the solution for (dy)/(dx)=18sqrt(xy) ?

The solution for (dy)/(dx)=18sqrt(xy) is y=36x^3+6c_{1}x^{3/2}+(c_{1}^2)/4

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(dy)/(dx)=18sqrt(xy)

\frac{d y}{d x} = 18 x y

y = 36 x^{3} + 6 c_{1} x^{\frac{3}{2}} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = 18 x y

Solve separable ODE:

y = 36 x^{3} + 6 c_{1} x^{\frac{3}{2}} + \frac{c _{1}^{2}}{4}

y = 36 x^{3} + 6 c_{1} x^{\frac{3}{2}} + \frac{c _{1}^{2}}{4}

tan^{2} (x) cos^{2} (y) d x = d y

\frac{d y}{d x} = \frac{- 6}{4} x^{5} y^{8}

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

x \frac{d y}{d x} = \frac{1 - 4 y ^{2}}{3 y}

\frac{d y}{d x} y = 5^{x}

What is the solution for (dy)/(dx)=18sqrt(xy) ?
The solution for (dy)/(dx)=18sqrt(xy) is y=36x^3+6c_{1}x^{3/2}+(c_{1}^2)/4