The solutions to an inhomogeneous equation, if they exist, are obtained by starting with a particular solution and adding any solution to the homogeneous equation. Linear differential operators of order n. Section 3.2 . Existence and uniqueness for appropriate initial conditions. A homogeneous equation has an n-dimensional space of solutions if no initial conditions are specified. Section 3.3 .
Complex numbers help solve problems involving real numbers.
Section 3.5 . Great when it works. Sections 3.4, 3.6 . Section 4.1 plus a bit more stuff. An n th order equation in one variable reduces to a first order system in n variables.