What is the solution for (dy)/(dx)=6y^{2/3} ?

The solution for (dy)/(dx)=6y^{2/3} is y=8x^3+4c_{1}x^2+(2c_{1}^2x)/3+(c_{1}^3)/(27)

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(dy)/(dx)=6y^{2/3}

\frac{d y}{d x} = 6 y^{\frac{2}{3}}

y = 8 x^{3} + 4 c_{1} x^{2} + \frac{2 c _{1}^{2} x}{3} + \frac{c _{1}^{3}}{27}

Solution steps

\frac{d y}{d x} = 6 y^{\frac{2}{3}}

Solve separable ODE:

y = 8 x^{3} + 4 c_{1} x^{2} + \frac{2 c _{1}^{2} x}{3} + \frac{c _{1}^{3}}{27}

y = 8 x^{3} + 4 c_{1} x^{2} + \frac{2 c _{1}^{2} x}{3} + \frac{c _{1}^{3}}{27}

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What is the solution for (dy)/(dx)=6y^{2/3} ?
The solution for (dy)/(dx)=6y^{2/3} is y=8x^3+4c_{1}x^2+(2c_{1}^2x)/3+(c_{1}^3)/(27)