What is the solution for y^'=(64xy)^{1/3} ?

The solution for y^'=(64xy)^{1/3} is

y^'=(64xy)^{1/3}

y^{^{'}} = (64 x y)^{\frac{1}{3}}

y = \frac{2 2 27 x ^{4} + 27 c _{1} x ^{\frac{8}{3}} + 9 c _{1}^{2} x ^{\frac{4}{3}} + c _{1}^{3}}{3 3}, y = - \frac{2 2 27 x ^{4} + 27 c _{1} x ^{\frac{8}{3}} + 9 c _{1}^{2} x ^{\frac{4}{3}} + c _{1}^{3}}{3 3}

Solution steps

y^{'} (x) = (64 x y)^{\frac{1}{3}}

Solve separable ODE:

y = \frac{2 2 27 x ^{4} + 27 c _{1} x ^{\frac{8}{3}} + 9 c _{1}^{2} x ^{\frac{4}{3}} + c _{1}^{3}}{3 3}, y = - \frac{2 2 27 x ^{4} + 27 c _{1} x ^{\frac{8}{3}} + 9 c _{1}^{2} x ^{\frac{4}{3}} + c _{1}^{3}}{3 3}

y = \frac{2 2 27 x ^{4} + 27 c _{1} x ^{\frac{8}{3}} + 9 c _{1}^{2} x ^{\frac{4}{3}} + c _{1}^{3}}{3 3}, y = - \frac{2 2 27 x ^{4} + 27 c _{1} x ^{\frac{8}{3}} + 9 c _{1}^{2} x ^{\frac{4}{3}} + c _{1}^{3}}{3 3}

d er i v a t i v e y = \frac{x}{2}

d er i v a t i v e \frac{9}{x ^{3}}

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\frac{\partial}{\partial x} (\frac{sin ( y )}{x ^{2} + 1})

\int 10 x - x^{2} d x

What is the solution for y^'=(64xy)^{1/3} ?
The solution for y^'=(64xy)^{1/3} is