What is the solution for (dy)/(dx)=x^3sqrt(6y) ?

The solution for (dy)/(dx)=x^3sqrt(6y) is y=(3x^8}{32}+(sqrt(3)c_{1}x^4)/(4sqrt(2))+\frac{c_{1}^2)/4

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(dy)/(dx)=x^3sqrt(6y)

\frac{d y}{d x} = x^{3} 6 y

y = \frac{3 x ^{8}}{32} + \frac{3 c _{1} x ^{4}}{4 2} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = x^{3} 6 y

Solve separable ODE:

y = \frac{3 x ^{8}}{32} + \frac{3 c _{1} x ^{4}}{4 2} + \frac{c _{1}^{2}}{4}

y = \frac{3 x ^{8}}{32} + \frac{3 c _{1} x ^{4}}{4 2} + \frac{c _{1}^{2}}{4}

\frac{d S}{d t} = 0.05 - \frac{S}{( \frac{945}{2} )}

\frac{d x}{d t} = 4 x t^{2}

\frac{d y}{d t} = k (a - y)

\frac{d y}{d x} + e^{(x + y)} = 0

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

What is the solution for (dy)/(dx)=x^3sqrt(6y) ?
The solution for (dy)/(dx)=x^3sqrt(6y) is y=(3x^8}{32}+(sqrt(3)c_{1}x^4)/(4sqrt(2))+\frac{c_{1}^2)/4