Boundary Value Problems/Solving inhomogeneous linear ODEs

${\displaystyle \displaystyle y''+p(t)y'+q(t)y=f(t)}$ is a second order linear inhomogeneous differential equation. ${\displaystyle f(t)\neq 0}$ for the complete interval ${\displaystyle t\in [c,d]}$. An example: ${\displaystyle \displaystyle 2y''+3y'+y=sin(2t)}$ .
General information on Ordinary Differential Equations may be found at [Ordinary Differential Equations http://en.wikipedia.org/wiki/Ordinary_differential_equation]. We are interested in a specific type: One where the coefficients are constants. ${\displaystyle \displaystyle ay''+by'+cy=f(t)}$.