What is the solution for (dy)/(dx)=20sqrt(xy) ?

The solution for (dy)/(dx)=20sqrt(xy) is y=(400x^3)/9+(20c_{1}x^{3/2})/3+(c_{1}^2)/4

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(dy)/(dx)=20sqrt(xy)

\frac{d y}{d x} = 20 x y

y = \frac{400 x ^{3}}{9} + \frac{20 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = 20 x y

Solve separable ODE:

y = \frac{400 x ^{3}}{9} + \frac{20 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

y = \frac{400 x ^{3}}{9} + \frac{20 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

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

\frac{d y}{d x} = \frac{( x - 8 )}{64 y - 384}

x y^{^{'}} + y ln (y) = 0

(x^{2} - 1) y^{^{'}} = y

\frac{d y}{d x} y = u, u = x^{2} + 10

What is the solution for (dy)/(dx)=20sqrt(xy) ?
The solution for (dy)/(dx)=20sqrt(xy) is y=(400x^3)/9+(20c_{1}x^{3/2})/3+(c_{1}^2)/4