What is the solution for x^'=3x^{2/3} ?

The solution for x^'=3x^{2/3} is x=t^3+c_{1}t^2+(c_{1}^2t)/3+(c_{1}^3)/(27)

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x^'=3x^{2/3}

x^{^{'}} = 3 x^{\frac{2}{3}}

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

Solution steps

x^{'} (t) = 3 x^{\frac{2}{3}}

Solve separable ODE:

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

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

What is the solution for x^'=3x^{2/3} ?
The solution for x^'=3x^{2/3} is x=t^3+c_{1}t^2+(c_{1}^2t)/3+(c_{1}^3)/(27)