4.13.2.5 Example 5

\begin{equation} \left ( y^{\prime }\right ) ^{2}=y\left ( y-2y^{\prime }x\right ) ^{3} \tag {1}\end{equation}

One way to handle this is to first solve for \(y^{\prime }\) and then apply the above method. This will result in \(m=-1\).