diff --git a/aufgaben/1/10000002.tex b/aufgaben/1/10000002.tex
index e9c1376..931d2f2 100644
--- a/aufgaben/1/10000002.tex
+++ b/aufgaben/1/10000002.tex
@@ -31,10 +31,10 @@
 \]
 The general solution of the differential equation now becomes
 \[
-y(x)=\frac12x^2+Ax+B, \text{\quad mit\quad} y'(x)=x+A.
+y(x)=\frac12x^2+Ax+B, \text{\quad with \quad} y'(x)=x+A.
 \]
 The values and derivatives of the solution at the interval ends are
-\begin{center} 
+\begin{center}
 \begin{tabular}{|c|cc|}
 \hline
 &0&1\\
diff --git a/aufgaben/2/20000002.tex b/aufgaben/2/20000002.tex
index 9180399..75cce42 100644
--- a/aufgaben/2/20000002.tex
+++ b/aufgaben/2/20000002.tex
@@ -16,7 +16,7 @@
 This is a half plane that includes the $y$-axis.
 The points on the $y$-axis are boundary points, any small neighborhood of
 these points has points in $\Omega$ and points outside of it.
-So $\Omega$ ist not open and therefore not a domain.
+So $\Omega$ is not open and therefore not a domain.
 (figure \ref{20000002:fig} left).
 \item
 $\Omega$ consists of all points except the origin.
@@ -41,7 +41,7 @@
 \includeagraphics[]{graphs-2}
 \end{center}
 \caption{Subsets $\Omega\subset\mathbb R^2$ for problem \ref{20000002} a)
-(left) 
+(left)
 and b) (right)\label{20000002:fig}}
 \end{figure}
 \end{loesung}