What is the solution for (dy)/(dx)=2x^3sqrt(y) ?

The solution for (dy)/(dx)=2x^3sqrt(y) is y=(x^8}{16}+\frac{c_{1}x^4)/4+(c_{1}^2)/4

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(dy)/(dx)=2x^3sqrt(y)

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

y = \frac{x ^{8}}{16} + \frac{c _{1} x ^{4}}{4} + \frac{c _{1}^{2}}{4}

Solution steps

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

Solve separable ODE:

y = \frac{x ^{8}}{16} + \frac{c _{1} x ^{4}}{4} + \frac{c _{1}^{2}}{4}

y = \frac{x ^{8}}{16} + \frac{c _{1} x ^{4}}{4} + \frac{c _{1}^{2}}{4}

(x^{2} + 1) \frac{d y}{d x} + 3 x y = 3 x

\frac{d y}{d x} y = 2 x^{2} - 13 x + 6

\frac{d y}{d x} = \frac{( x + x y ^{2} )}{4 y}

\frac{d y}{d x} = \frac{6 x ^{2} + 4}{8 y ^{3} + 1}, y (0) = 1

- y^{^{'}} = - 2 yy

What is the solution for (dy)/(dx)=2x^3sqrt(y) ?
The solution for (dy)/(dx)=2x^3sqrt(y) is y=(x^8}{16}+\frac{c_{1}x^4)/4+(c_{1}^2)/4