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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{\partial}{\partial y} (2 x y^{4} + 2)

x \to 0 lim (\frac{1}{2 x})

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

\int_{\frac{1}{2}}^{1} \frac{4 y + 5}{y ^{2} + y} d y

\int_{- 5}^{5} \frac{1}{x ^{(\frac{2}{3})}} d x

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