First-Order Differential Equations

Learn to solve first-order ordinary differential equations through comprehensive study of fundamental concepts and solution methods. Master the classification and identification of different types of first-order differential equations, including separable, linear, exact, and Bernoulli equations. Develop proficiency in applying appropriate analytical techniques such as separation of variables, integrating factors, and substitution methods to find solutions. Explore the geometric interpretation of differential equations through direction fields and solution curves. Practice solving real-world application problems involving population growth, radioactive decay, cooling processes, and mixing problems. Gain understanding of existence and uniqueness theorems for initial value problems and learn to verify solutions through substitution and graphical analysis.