Solve the differential equation:

To solve the given differential equation \( 2x\frac{dy}{dx} + y(6y^2 - x - 1) = 0 \), we can follow these steps:

1. First, we'll rearrange the equation to separate variables.
2. Then, we'll integrate both sides to solve for y.

Let's begin by rearranging the equation:

\[ 2x \frac{dy}{dx} = -y(6y^2 - x - 1) \]

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