Add up to figure on page 6

src/differential_equations_2.md

@@ -334,6 +334,22 @@ To summarize, this process has broken one partial differential equation into two
 ordinary differential equations of different variables. In order to do this, we 
 needed to introduce a separation constant, which remains to be determined.
 
+### Boundary and eigenvalue problems ###
+
+Continuing on with the Schr\"{o}dinger equation example from the previous 
+section, let us focus on 
+
+$$-\frac{\hbar^2}{2m} \phi''(x) = \lambda \phi(x),$$
+$$\phi(0)=\phi(L)=0.$$
+
+This has the form of an eigenvalue equation, in which $\lambda$ is the 
+eigenvalue, $- \frac{\hbar^2}{2m} \frac{d^2}{dx^2}[\cdot]$ is the linear 
+operator and $\phi(x)$ is the eigenfunction. 
+
+Notice that when stating the ordinary differential equation, it is specified 
+along with it's boundary conditions. Note that in contrast to an initial value
+problem, a boundary value problem does not always have a solution. 
+