Chapter 13 DE5: Non-Homogeneous Second Order Linear DEs
Recall that a 2nd order linear DE is a differential equation of the form
\begin{equation*}
P(x)y''+Q(x)y'+R(x)y=f(x)
\end{equation*}
If the functions \(P\text{,}\) \(Q\) and \(R\) are all constant functions then the DE is said to have constant coefficients. If \(f(x)=0\) then the DE is said to be homogeneous. In the previous lecture (i.e. Chapter 12) we discussed how to find solutions to a second order linear homogeneous DE with constant coefficients, i.e. to a DE of the form
\begin{equation*}
ay''+by'+c=0
\end{equation*}
In this lecture we are going to look at solving some non-homogeneous second order linear DEs with constant coefficients, i.e. DEs of the form
\begin{equation*}
ay''+by'+c=f(x)
\end{equation*}
Some insight into how we might solve such DEs can be gained by revisiting some relevant first order examples.