Second Order Equations: Polynomial, Trigonometric, and Exponential Cases

This lecture covers the solutions of second-order differential equations with polynomial, trigonometric, and exponential forcing functions. It explains the method to find particular solutions using the same form as the forcing function. The lecture also delves into the cases of polynomial forcing functions, such as tn, and trigonometric functions like sin wt. It demonstrates the process of solving the differential equations step by step, providing insights into the unique solutions based on the coefficients. Additionally, it explores the characteristic equation and its roots in the exponential case, highlighting the different scenarios that arise based on the discriminant value.