What is the solution for (dy)/(dx)=4x^3sqrt(y) ?

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

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(dy)/(dx)=4x^3sqrt(y)

\frac{d y}{d x} = 4 x^{3} y

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

Solution steps

\frac{d y}{d x} = 4 x^{3} y

Solve separable ODE:

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

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

\int \frac{D ( 5 x ^{2} + 5 y ^{2} ) - 1}{2} d A

x y^{^{'}} + 2 y = 3 sin (x)

\int \frac{e ^{2 x}}{e ^{4 x} + 4} d x

\int_{1}^{\infty} e^{- 5 x} d x

\frac{d}{d x} (3 - 4 sin (2 x + \frac{π}{4}))

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