What is the solution for (dy)/(dx)=6x(y-1)^{2/3} ?

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

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(dy)/(dx)=6x(y-1)^{2/3}

\frac{d y}{d x} = 6 x (y - 1)^{\frac{2}{3}}

y = x^{6} + c_{1} x^{4} + \frac{c _{1}^{2} x ^{2}}{3} + \frac{c _{1}^{3}}{27} + 1

Solution steps

\frac{d y}{d x} = 6 x (y - 1)^{\frac{2}{3}}

Solve separable ODE:

y = x^{6} + c_{1} x^{4} + \frac{c _{1}^{2} x ^{2}}{3} + \frac{c _{1}^{3}}{27} + 1

y = x^{6} + c_{1} x^{4} + \frac{c _{1}^{2} x ^{2}}{3} + \frac{c _{1}^{3}}{27} + 1

\int \frac{x ^{3} - 6 x - 20}{x + 5} d x

t sin (π) t

x \to 3 lim (x^{2} - 5)

y^{^{'}} = \frac{( x + 3 y )}{2 x}

\int \frac{x ^{3} - 5 x ^{2} + 7}{x - 5} d x

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