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

The solution for (dy)/(dx)=y^{2/3} is y=(x^3}{27}+(c_{1}x^2)/9+(c_{1}^2x)/9+\frac{c_{1}^3)/(27)

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(dy)/(dx)=y^{2/3}

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

y = \frac{x ^{3}}{27} + \frac{c _{1} x ^{2}}{9} + \frac{c _{1}^{2} x}{9} + \frac{c _{1}^{3}}{27}

Solution steps

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

Solve separable ODE:

y = \frac{x ^{3}}{27} + \frac{c _{1} x ^{2}}{9} + \frac{c _{1}^{2} x}{9} + \frac{c _{1}^{3}}{27}

y = \frac{x ^{3}}{27} + \frac{c _{1} x ^{2}}{9} + \frac{c _{1}^{2} x}{9} + \frac{c _{1}^{3}}{27}

What is the solution for (dy)/(dx)=y^{2/3} ?
The solution for (dy)/(dx)=y^{2/3} is y=(x^3}{27}+(c_{1}x^2)/9+(c_{1}^2x)/9+\frac{c_{1}^3)/(27)