What is the solution for (dy)/(dx)=\sqrt[3]{x(y-1)} ?

The solution for (dy)/(dx)=\sqrt[3]{x(y-1)} is

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(dy)/(dx)=\sqrt[3]{x(y-1)}

y = \frac{27 x ^{4} + 108 c _{1} x ^{\frac{8}{3}} + 144 c _{1}^{2} x ^{\frac{4}{3}} + 64 c _{1}^{3}}{6 6} + 1, y = - \frac{27 x ^{4} + 108 c _{1} x ^{\frac{8}{3}} + 144 c _{1}^{2} x ^{\frac{4}{3}} + 64 c _{1}^{3}}{6 6} + 1

Solution steps

Solve separable ODE:

y = \frac{27 x ^{4} + 108 c _{1} x ^{\frac{8}{3}} + 144 c _{1}^{2} x ^{\frac{4}{3}} + 64 c _{1}^{3}}{6 6} + 1, y = - \frac{27 x ^{4} + 108 c _{1} x ^{\frac{8}{3}} + 144 c _{1}^{2} x ^{\frac{4}{3}} + 64 c _{1}^{3}}{6 6} + 1

y = \frac{27 x ^{4} + 108 c _{1} x ^{\frac{8}{3}} + 144 c _{1}^{2} x ^{\frac{4}{3}} + 64 c _{1}^{3}}{6 6} + 1, y = - \frac{27 x ^{4} + 108 c _{1} x ^{\frac{8}{3}} + 144 c _{1}^{2} x ^{\frac{4}{3}} + 64 c _{1}^{3}}{6 6} + 1

\frac{d x}{d t} = 5000 + 0.04 x, x = 18000, t = 0

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

\frac{d y}{d t} = 3 - 0.04 y

\frac{x y + 3 x - y - 3}{x y - 2 x + 4 y - 8} = \frac{d y}{d x}

(t^{2} - 14 t + 45) \frac{d y}{d t} = y

What is the solution for (dy)/(dx)=\sqrt[3]{x(y-1)} ?
The solution for (dy)/(dx)=\sqrt[3]{x(y-1)} is