  The aim of this paper is the analysis, from algebraic point of view and
singularities studies, of the 5-parametric family of differential equations
  \begin{equation*}\label{folpz}
  yy'=(\alpha x^{m+k-1}+\beta x^{m-k-1})y+\gamma x^{2m-2k-1}, \quad
y'=\frac{dy}{dx}
  \end{equation*}
  where $a,b,c\in \mathbb{C}$, $m,k\in \mathbb{Z}$ and
  $$\alpha=a(2m+k) \quad \beta=b(2m-k), \quad
\gamma=-(a^2mx^{4k}+cx^{2k}+b^2m).$$ This family is very important because
include Van Der Pol equation. Moreover, this family seems to appear as exercise
in the celebrated book of Polyanin and Zaitsev. Unfortunately, the exercise
presented a typo which does not allow to solve correctly it. We present the
corrected exercise, which corresponds to the title of this paper. We solve the
exercise and afterwards we make algebraic and of singularities studies to this
family of differential equations. To illustrate the qualitative and algebraic
techniques we present an example of a biparametric quadratic Polyanin-Zaitsev
vector field.
