diff --git a/src/8_differential_equations_2.md b/src/8_differential_equations_2.md
index 7d543f55a2e1578755594ca9817a02aa45221b84..33c482832a7ff25a21af2be83f6bcce8985fa537 100644
--- a/src/8_differential_equations_2.md
+++ b/src/8_differential_equations_2.md
@@ -283,7 +283,7 @@ to solving these equations, but the choice of technique must be tailored to the
 equation at hand. Hence we focus on some specific examples that are common in
 physics.
 
-## Separation of variables ##
+### Separation of variables
 
 Let us focus on the one dimensional Schrödinger equation of a free particle
 
@@ -332,7 +332,7 @@ 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 ###
+### Boundary and eigenvalue problems
 
 Continuing on with the Schrödinger equation example from the previous 
 section, let us focus on 
@@ -493,7 +493,7 @@ coefficient,
 
 $$c_n:= \int^{L}_{0} dx sin(\frac{n \pi x}{L}) \psi_{0}(x). $$
     
-## General recipie for seperable PDEs ##
+### General recipie for seperable PDEs
 
 1. Make the separation ansatz to obtain separate ordinary differential 
     equations.
@@ -518,62 +518,60 @@ possible approach is to try working in a different coordinate system. There are
 a few more analytic techniques available, however in many situations it becomes
 necessary to work with numerical methods of solution. 
 
-# Problems
+### Problems
 
 1.  [:grinning:] Which of the following equations for $y(x)$ is linear?
 
-        (a) y''' - y'' + x cos(x) y' + y - 1 = 0
+    (a) y''' - y'' + x cos(x) y' + y - 1 = 0
 
-        (b) y''' + 4 x y' - cos(x) y = 0
+    (b) y''' + 4 x y' - cos(x) y = 0
 
-        (c) y'' + y y' = 0
+    (c) y'' + y y' = 0
 
-        (d) y'' + e^x y' - x y = 0
+    (d) y'' + e^x y' - x y = 0
 
 2.  [:grinning:] Find the general solution to the equation 
 
-        $$y'' - 4 y' + 4 y = 0. $$
+    $$y'' - 4 y' + 4 y = 0. $$
 
-        Show explicitly by computing the Wronski determinant that the 
-        basis for the solution space is actually linearly independent. 
+    Show explicitly by computing the Wronski determinant that the 
+    basis for the solution space is actually linearly independent. 
 
 3.  [:grinning:] Find the general solution to the equation 
 
-        $$y''' - y'' + y' - y = 0.$$
+    $$y''' - y'' + y' - y = 0.$$
 
-        Then find the solution to the initial conditions $y''(0) =0$, $y'(0)=1$, $y(0)=0$. 
+    Then find the solution to the initial conditions $y''(0) =0$, $y'(0)=1$, $y(0)=0$. 
 
 4.  [:smirk:] Take the Laplace equation in 2D:
 
-        $$\frac{\partial^2 \phi(x,y)}{\partial x^2} + \frac{\partial^2 \phi(x,y)}{\partial y^2} = 0.$$
+    $$\frac{\partial^2 \phi(x,y)}{\partial x^2} + \frac{\partial^2 \phi(x,y)}{\partial y^2} = 0.$$
 
-        (a) Make a separation ansatz $\phi(x,y) = f(x)g(y)$ and write 
-          down the resulting ordinary differential equations.
+    (a) Make a separation ansatz $\phi(x,y) = f(x)g(y)$ and write 
+        down the resulting ordinary differential equations.
 
-        (b) Now assume that the boundary conditions $\phi(0,y) = \phi(L,y) =0$ for 
-          all y, i.e.  f(0)=f(L)=0. Find all solutions $f(x)$ and the corresponding 
-          eigenvalues.
+    (b) Now assume that the boundary conditions $\phi(0,y) = \phi(L,y) =0$ for 
+    	all y, i.e.  f(0)=f(L)=0. Find all solutions $f(x)$ and the
+	corresponding eigenvalues.
 
-        (c) Finally, for each eigenvalue, find the general solution $g(y)$ for this
-          eigenvalue. Combine this with all solutions $f(x)$ to write down the general
-          solution (we know from the lecture that the operator $\frac{d^2}{dx^2}$ is 
-          hermitian - you can thus directly assume that the solutions form an orthogonal
-          basis). 
+    (c) Finally, for each eigenvalue, find the general solution $g(y)$ for
+    	this eigenvalue. Combine this with all solutions $f(x)$ to write down
+	the general solution (we know from the lecture that the operator
+	$\frac{d^2}{dx^2}$ is Hermitian - you can thus directly assume that
+	the solutions form an orthogonal basis). 
 
 5.  [:smirk:] Take the partial differential equation
 
-        $$\frac{\partial h(x,y)}{\partial x} + x \frac{\partial h(x,y)}{\partial y} = 0. $$
+    $$\frac{\partial h(x,y)}{\partial x} + x \frac{\partial h(x,y)}{\partial y} = 0. $$
 
-        Try to make a separation ansatz $h(x,y)=f(x)g(y)$. What do you observe?
+    Try to make a separation ansatz $h(x,y)=f(x)g(y)$. What do you observe?
 
-6.  [:sweat:] *Bonus question - this kind of question will not be asked in the exam*
+6.  [:sweat:] We consider the Hilbert space of functions $f(x)$ defined
+    for $x \ \epsilon \ [0,L]$ with $f(0)=f(L)=0$. 
 
-        We consider the Hilbert space of functions $f(x)$ defined for $x \ \epsilon \ [0,L]$
-        with $f(0)=f(L)=0$. 
+    Which of the following operators on this space is hermitian?
 
-        Which of the following operators on this space is hermitian?
+    (a) Lf = A(x) \frac{d^2 f}{dx^2}
 
-        (a) Lf = A(x) \frac{d^2 f}{dx^2}
-
-        (b) Lf = \frac{d}{dx} \big{()} A(x) \frac{df}{dx} \big{)}
+    (b) Lf = \frac{d}{dx} \big{()} A(x) \frac{df}{dx} \big{)}