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

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

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

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

y = - x^{3} + \frac{x ^{6}}{216} - \frac{x ^{5}}{12} + \frac{c _{1} x ^{4}}{36} + \frac{x ^{4}}{2} + \frac{- c _{1} x ^{3} - c _{1}^{2} x}{3} + \frac{c _{1}^{2} x ^{2}}{18} + c_{1} x^{2} + \frac{c _{1}^{3}}{27} - 1

Solution steps

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

Solve separable ODE:

y = - x^{3} + \frac{x ^{6}}{216} - \frac{x ^{5}}{12} + \frac{c _{1} x ^{4}}{36} + \frac{x ^{4}}{2} + \frac{- c _{1} x ^{3} - c _{1}^{2} x}{3} + \frac{c _{1}^{2} x ^{2}}{18} + c_{1} x^{2} + \frac{c _{1}^{3}}{27} - 1

y = - x^{3} + \frac{x ^{6}}{216} - \frac{x ^{5}}{12} + \frac{c _{1} x ^{4}}{36} + \frac{x ^{4}}{2} + \frac{- c _{1} x ^{3} - c _{1}^{2} x}{3} + \frac{c _{1}^{2} x ^{2}}{18} + c_{1} x^{2} + \frac{c _{1}^{3}}{27} - 1

\int \frac{4 x}{( 2 x ^{2} - 8 ) ^{5}} d x

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

y y^{^{'}} = t^{2}, y (0) = 2

y^{^{'}} + 3 y = 1, y (0) = 1

\frac{d y}{d x}, x y = 30

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