\[y(1-y)\frac{{\partial}^{2}{F_{2}}}{{\partial y}^{2}}-xy\frac{\,{\partial}^{2}{%
F_{2}}}{\,\partial x\,\partial y}+\left(\gamma^{\prime}-(\alpha+\beta^{\prime}%
+1)y\right)\frac{\partial{F_{2}}}{\partial y}-\beta^{\prime}x\frac{\partial{F_%
{2}}}{\partial x}-\alpha\beta^{\prime}{F_{2}}=0,\]