diff --git a/src/8_differential_equations_2.md b/src/8_differential_equations_2.md
index 3309480fad8c800ebd7c18f3388822094dc05d09..b1034f92db4ab11d74e3628e7a91dfadaeb137e9 100644
--- a/src/8_differential_equations_2.md
+++ b/src/8_differential_equations_2.md
@@ -56,11 +56,11 @@ $$y_{1} = y, \ y_{2} = y', \ \cdots, \ y_{n} = y^{(n-1)}.$$
 Then, the differential equation can be re-written as
 
 $$\begin{split}
-y_1 ' & = & y_2 \\
-y_2 ' & = & y_3 \\
-& \vdots & \\
-y_{n-1} '& = & y_{n} \\
-y_{n} ' & = & - a_{0} y_{1} - a_{1} y_{2} - \cdots - a_{n-1} y_{n}.
+y_1 ' & = y_2 \\
+y_2 ' & = y_3 \\
+& \vdots \\
+y_{n-1} '& = y_{n} \\
+y_{n} ' & = - a_{0} y_{1} - a_{1} y_{2} - \cdots - a_{n-1} y_{n}.
 \end{split}$$
 
 Notice that together these $n$ equations form a linear first order system, the 
@@ -145,9 +145,9 @@ $$P(\lambda) = \lambda^n + a_{n-1} \lambda^{n-1} + \cdots + a_0.$$
       + a_0$$
     $$- \det(A - \lambda I) = P(\lambda).$$
 
-In the second last line of the proof we indicated that the method of co-factor 
-expansion demonstrated is repeated an additional $n-2$ times. This completes the
-proof. 
+    In the second last line of the proof we indicated that the method of
+    co-factor  expansion demonstrated is repeated an additional $n-2$ times.
+    This completes the proof. 
 
 With the characteristic polynomial, it is possible to write the differential 
 equation as