diff --git a/docs/examples/chap_05.ipynb b/docs/examples/chap_05.ipynb
index 1327502..7e441d3 100644
--- a/docs/examples/chap_05.ipynb
+++ b/docs/examples/chap_05.ipynb
@@ -21,7 +21,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -72,7 +72,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
@@ -85,7 +85,7 @@
        "[2⋅cos(2⋅t), -2⋅sin(2⋅t)]"
       ]
      },
-     "execution_count": 33,
+     "execution_count": 2,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -129,7 +129,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -152,7 +152,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -198,22 +198,24 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "$$\n",
     "\\begin{align*}\n",
     "\\frac{dR}{dt} &= \\frac{1}{0.02}(-R + S(P)) \\\\ \n",
     "S(P) &= \\begin{cases}\n",
     "\\frac{100P^2}{25 + P^2} & \\text{for } P \\geq 0 \\\\\n",
     "0 & \\text{for } P < 0\n",
     "\\end{cases} \\\\\n",
-    "\n",
     "P(t) &= 20\\sin(2\\pi10t)\n",
     "\\end{align*}\n",
+    "$$\n",
+    "\n",
     "\n",
     "where $R(0)=0, T=1, h=0.004$."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -244,7 +246,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {