Worked on enhancing the mphowardlab/essential-math repository by developing comprehensive documentation for the substitution method used in solving second-order ordinary differential equations. Focused on technical writing and differential equations, the work involved creating a new Markdown section that guides users through the substitution technique, supported by detailed worked examples in kinematics and incompressible flow within a cylinder. The documentation was structured using LaTeX and Markdown to ensure clarity and accessibility, and the table of contents was updated to improve navigation. These contributions aimed to streamline onboarding and increase the discoverability of advanced mathematical methods for users of the repository.