The recent developments in the computational methods for solving differential equations have shown a shift towards more efficient and accurate techniques, particularly in handling stiff systems and singular integrals. The field is witnessing advancements in explicit exponential integration methods, which aim to address the computational challenges posed by stiff ordinary differential equations (ODEs) without resorting to computationally expensive implicit methods. These methods leverage the matrix exponential to maintain stability while reducing computational costs, though they currently face limitations in accuracy and scalability. Additionally, there is a growing interest in the development of numerical methods for singular integrals, with a focus on integrating by parts to transform singular integrals into non-singular forms, thereby enhancing computational efficiency and accuracy. Notably, these methods are proving effective even when the exact form of the singular integrand is unknown, broadening their applicability. The integration of GPU-accelerated ODE solvers into open-source frameworks is also a significant trend, facilitating the accessibility and scalability of these tools in complex differentiable programs. Overall, the field is progressing towards more efficient, scalable, and accurate methods for solving differential equations, with a particular emphasis on handling stiffness and singularities.