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