What is the solution for (dy)/(dx)=y^{2/3},y(1)=8 ?

The solution for (dy)/(dx)=y^{2/3},y(1)=8 is y=(x^3}{27}+\frac{5x^2)/9+(25x)/9+125/27

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(dy)/(dx)=y^{2/3},y(1)=8

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

y = \frac{x ^{3}}{27} + \frac{5 x ^{2}}{9} + \frac{25 x}{9} + \frac{125}{27}

Solution steps

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

Solve separable ODE:

y = \frac{x ^{3}}{27} + \frac{5 x ^{2}}{9} + \frac{25 x}{9} + \frac{125}{27}

y = \frac{x ^{3}}{27} + \frac{5 x ^{2}}{9} + \frac{25 x}{9} + \frac{125}{27}

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What is the solution for (dy)/(dx)=y^{2/3},y(1)=8 ?
The solution for (dy)/(dx)=y^{2/3},y(1)=8 is y=(x^3}{27}+\frac{5x^2)/9+(25x)/9+125/27