Edit problem 1 and add problem 3

latex/problems/problem1.tex

@@ -1,8 +1,17 @@
 \section*{Problem 1}
 
+First, we rearrange the equation.
+
+\begin{align*}
+    - \frac{d^2u}{dx^2} &= 100 e^{-10x} \\
+    \frac{d^2u}{dx^2} &= -100 e^{-10x} \\
+\end{align*}
+
+Now we find $u(x)$.
+
 % Do the double integral
 \begin{align*}
-    u(x) &= \int \int \frac{d^2 u}{dx^2} dx^2\\
+    u(x) &= \int \int \frac{d^2 u}{dx^2} dx^2 \\
          &= \int \int -100 e^{-10x} dx^2 \\
          &= \int \frac{-100 e^{-10x}}{-10} + c_1 dx \\
          &= \int 10 e^{-10x} + c_1 dx \\
@@ -10,7 +19,7 @@
          &= -e^{-10x} + c_1 x + c_2
 \end{align*}
 
-Using the boundary conditions, we can find $c_1$ and $c_2$ as shown below:
+Using the boundary conditions, we can find $c_1$ and $c_2$
 
 \begin{align*}
     u(0) &= 0 \\