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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d}{d x} (\frac{( x - 1 ) ^{2}}{x + 2})

\int (e^{2 x} + x) d x

- 0.0000272 x^{2} + 0.008459 x + 440

x \to \infty lim (- \frac{4 x}{5})

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2}}{x - 1})

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