2. Solve: z dy (6r + 1)y+ 3r² + 2y* = 0 dr

The given differential equation is $(6x+1)y^2\frac{dy}{dx}+3x^2+2y^3=0$.

Divide both sides of the given equation by $6x+1$ and rearrange the terms to obtain the Bernoulli equation.

$\begin{array}{rcl}{y}^2\frac{dy}{dx}+\frac{3x^2}{6x+1}+\frac{2y^3}{6x+1}& =& 0\\ y^2\frac{dy}{dx}+\frac{2}{6x+1}{y}^3& =& -\frac{3x^2}{6x+1}\end{array}$