fix math errors

src/8_differential_equations_2.md

@@ -536,13 +536,13 @@ necessary to work with numerical methods of solution.
 
 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 
 
@@ -576,9 +576,9 @@ necessary to work with numerical methods of solution.
 
 5.  [:smirk:] Consider the following partial differential equations, and try to make a separation ansatz $h(x,y)=f(x)g(y)$. What do you observe in each case? (Only attempt the separation, do not solve the problem fully)
 
-    (a) $$\frac{\partial h(x,y)}{\partial x} + x \frac{\partial h(x,y)}{\partial y} = 0. $$
+    (a) $\frac{\partial h(x,y)}{\partial x} + x \frac{\partial h(x,y)}{\partial y} = 0. $
 
-    (b) $$\frac{\partial h(x,y)}{\partial x} + \frac{\partial h(x,y)}{\partial y} + xy\,h(x,y) = 0$$
+    (b) $\frac{\partial h(x,y)}{\partial x} + \frac{\partial h(x,y)}{\partial y} + xy\,h(x,y) = 0$
 
 6.  [:sweat:] We consider the Hilbert space of functions $f(x)$ defined
     for $x \ \epsilon \ [0,L]$ with $f(0)=f(L)=0$.