Linear Differential Equations: Constant Coefficients and Solution Methods

This lecture discusses a specific category of linear difference equations with constant coefficients. The instructor presents a comprehensive resolution method for these equations, focusing on the exponential function as a solution. The lecture begins by defining linear equations with constant coefficients and illustrates how to derive their general solutions. The instructor emphasizes the importance of identifying the form of the solution based on the second member of the equation. A key concept introduced is the 'method of good choice,' which allows for the anticipation of the solution's form without fully resolving the integral. The lecture further explores cases where the second member is an exponential function, detailing how to derive particular solutions. The instructor also addresses scenarios involving trigonometric and polynomial functions, providing general formulas for these cases. The lecture concludes by summarizing the approach to solving a wide range of differential equations with constant coefficients, setting the stage for practical examples in subsequent videos.