What is the solution for (dy)/(dx)=\sqrt[3]{x(y-1)},y(0)=1 ?

The solution for (dy)/(dx)=\sqrt[3]{x(y-1)},y(0)=1 is y=(x^2)/(2sqrt(2))+1,y=-(x^2)/(2sqrt(2))+1

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(dy)/(dx)=\sqrt[3]{x(y-1)},y(0)=1

y = \frac{x ^{2}}{2 2} + 1, y = - \frac{x ^{2}}{2 2} + 1

Solution steps

Solve separable ODE:

y = \frac{x ^{2}}{2 2} + 1, y = - \frac{x ^{2}}{2 2} + 1

y = \frac{x ^{2}}{2 2} + 1, y = - \frac{x ^{2}}{2 2} + 1

y^{^{'}} = \frac{21 x}{y}

\frac{d t}{d y} = (2 t y^{2})

\frac{d y}{d x} = - 7 x y^{3}

(x^{2} + 4) y^{^{'}} + x y = 9 x

y (1 + x^{3}) y^{^{'}} + x^{2} (1 + y^{2}) = 0

What is the solution for (dy)/(dx)=\sqrt[3]{x(y-1)},y(0)=1 ?
The solution for (dy)/(dx)=\sqrt[3]{x(y-1)},y(0)=1 is y=(x^2)/(2sqrt(2))+1,y=-(x^2)/(2sqrt(2))+1