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--- howto:hambasics:sections:test [2021/01/04 22:00] – [Differential Equations] va7fi
+++ howto:hambasics:sections:test [2021/01/06 20:47] – [Differential Equations] va7fi
@@ Line 318: / Line 318: @@
 <WRAP center round info 80%>
-A differential equation is an equation that relates a function to its derivatives in some ways and the question is: given some information about the system, what's the function (or family of functions) that satisfy the differential equation.
+  * A differential equation is an equation that relates a function to its derivatives in some ways and the question is: given some information about the system, what's the function (or family of functions) that satisfy the differential equation.
-In physics we often use a dot above the function to indicate a derivative with respect to time, where as in math, we'll often use an apostrophe.  Physicists don't like the apostrophe too much because they sometimes use it to denote a different coordinate system.  So don't let the notation confuse you:
+  * In physics we often use a dot above the function to indicate a derivative with respect to time, where as in math, we'll often use an apostrophe.  Physicists don't like the apostrophe too much because they sometimes use it to denote a different coordinate system.  So don't let the notation confuse you:
 \$$ \dot{x}(t) = x'(t) = \frac{dx}{dt} \quad \text{and} \quad \ddot{x}(t) = x''(t) = \frac{d^2x}{dt^2} \$$
 </WRAP>
@@ Line 358: / Line 358: @@
 \$r\$ then:
-\$$ r = \left\{ \begin{array}{rl} -\alpha \pm \beta & \text{if } b^2 - 4ac > 0,\\
+\$$ r = \left\{ \begin{array}{ll} -\alpha \pm \beta & \text{if } b^2 - 4ac > 0,\\
  -\alpha \pm i \beta & \text{if } b^2 - 4ac < 0, \end{array} \right. \$$