What is the solution for (dy)/(dx)=y^{(1/3)} ?

The solution for (dy)/(dx)=y^{(1/3)} is

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(dy)/(dx)=y^{(1/3)}

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

y = \frac{2 2 x ^{3} + c _{1}^{3} + 3 c _{1} x ^{2} + 3 c _{1}^{2} x}{3 3}, y = - \frac{2 2 x ^{3} + c _{1}^{3} + 3 c _{1} x ^{2} + 3 c _{1}^{2} x}{3 3}

Solution steps

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

Solve separable ODE:

y = \frac{2 2 x ^{3} + c _{1}^{3} + 3 c _{1} x ^{2} + 3 c _{1}^{2} x}{3 3}, y = - \frac{2 2 x ^{3} + c _{1}^{3} + 3 c _{1} x ^{2} + 3 c _{1}^{2} x}{3 3}

y = \frac{2 2 x ^{3} + c _{1}^{3} + 3 c _{1} x ^{2} + 3 c _{1}^{2} x}{3 3}, y = - \frac{2 2 x ^{3} + c _{1}^{3} + 3 c _{1} x ^{2} + 3 c _{1}^{2} x}{3 3}

\int_{0}^{7} 7 - x d x

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\int 3 x^{2} (x - 2) (x + 3) d x

(1 + x^{2}) \frac{d y}{d x} - (2 x y + x^{2} + x^{4}) = 0

\frac{d x}{d t} - \frac{2}{3 t} x = 4 t x^{- 5}

What is the solution for (dy)/(dx)=y^{(1/3)} ?
The solution for (dy)/(dx)=y^{(1/3)} is