# Higher Order Linear Differential Equations with Constant Coefficients

1st Stage: The Solution of the Homogeneous Equation

Case A: The characteristic equation has n real roots:

Case B: The characteristic equation has n multiple real roots of multiplicity q:

Case C: The characteristic equation has complex roots:

Case D: Combination of the above cases

2nd Stage: The Partial Solution

Case B: Exponential-Polynomial Function

Case C: Trigonometric Function

Case D: Combination of the previous cases