What is the solution for y^'=(y^3+1)/((3xy^2)) ?

The solution for y^'=(y^3+1)/((3xy^2)) is y=\sqrt[3]{c_{1}x-1}

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y^'=(y^3+1)/((3xy^2))

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

y = 3 c_{1} x - 1

Solution steps

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

Solve separable ODE:

y = 3 c_{1} x - 1

y = 3 c_{1} x - 1

\frac{\partial}{\partial x} (3 x y^{2})

\frac{d}{d x} (4 x^{3} y^{3})

\frac{d y}{d x}, y^{4} = x

\frac{\partial}{\partial x} (- 2 cos (3 x))

\int_{0}^{1} \frac{1}{1 + x} d x

What is the solution for y^'=(y^3+1)/((3xy^2)) ?
The solution for y^'=(y^3+1)/((3xy^2)) is y=\sqrt[3]{c_{1}x-1}