\[\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}=\frac{1}{2w}\left(\frac{\mathrm{d}%
w}{\mathrm{d}z}\right)^{2}+\frac{3}{2}w^{3}+4zw^{2}+2(z^{2}-\alpha)w+\frac{%
\beta}{w},\]