MA 262: 1.6 Review- Substitution Methods & Exact Equations

Review of lesson 1.6 for MA 262 (Linear Algebra & Differential Equations) at Purdue University. Content based on class textbook Differential Equations & Linear Algebra by C. Henry Edwards and David E. Penney (ISBN: 9780536264923). 1.6 covers substitutions methods to solve differential equations (DEs) + methods to solve exact equations. Notable subtopics include: v-substitution, Bernoulli equations, exact equations, and second-order reducible differential equations. Derivation of v-substitution method is demonstrated for homogeneous linear DEs (criteria also specified), form of Bernoulli equations and appropriate substitution to solve is shown. The meaning and form of an exact equation are demonstrated, as well as the procedure to determine exactness and to solve exact equations. Second-order reducible equations are defined, and methods to reduce/solve are demonstrated for the two main cases (x missing vs. y missing). Example problems with work to solve are provided throughout.