TeX source:

\begin{aligned} \mathscr{L}_{y} R(x, y)=& \frac{1}{\alpha} \frac{\partial_{y} G(x, y)}{\{1+G(x, y)\}^{2}} \\ & \times\left[\alpha \int_{x}^{y} e^{\alpha(t-x)} D(t) d t-\left\{e^{\alpha(y-x)} D(y)-D(x)\right\}\right] \\ &-\frac{1}{\alpha} D^{\prime}(y)+\frac{1}{\alpha} \frac{e^{\alpha(y-x)} D^{\prime}(y)}{\{1+G(x, y)\}} \\ &+\frac{1}{\alpha} f(y) D(y)\left\{\frac{e^{\alpha(y-x)}}{1+G(x, y)}-1\right\}. \end{aligned}