<?xml version="1.0" encoding="UTF-8"?>
<Worksheet><Version major="6" minor="1"/><View-Properties><Zoom percentage="100"/></View-Properties><Styles><Layout alignment="left" bullet="none" firstindent="0.0" leftmargin="0.0" linebreak="space" linespacing="0.0" name="Normal" rightmargin="0.0" spaceabove="0.0" spacebelow="0.0"/><Layout alignment="centred" bullet="none" linespacing="0.5" name="Maple Output"/><Font background="[0,0,0]" bold="true" executable="true" family="Monospaced" foreground="[255,0,0]" name="Maple Input" opaque="false" size="12"/><Font background="[0,0,0]" bold="false" executable="false" family="Lucida Bright" foreground="[0,0,0]" italic="false" name="Text" opaque="false" size="12" underline="false"/><Font background="[0,0,0]" family="Lucida Bright" foreground="[0,0,255]" name="2D Output" opaque="false" readonly="true" size="12"/></Styles><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"/></Input></Group><Group><Input><Text-field layout="Normal" style="Text"><Font size="24">Template Worksheet:  Section 1.1</Font></Text-field><Text-field layout="Normal" style="Text">Verify that the given function satisfies the given differential equation:</Text-field><Text-field layout="Normal" style="Text"/><Text-field layout="Normal" style="Text">y(x)=exp(3x)cos(2x),   ODE:  y''-6y'+13y=0</Text-field><Text-field layout="Normal" style="Text"/><Text-field layout="Normal" style="Text"/></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">Y:=exp(3*x)*cos(2*x);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSJZRzYiKiYtSSRleHBHNiRJKnByb3RlY3RlZEdGKkkoX3N5c2xpYkdGJTYjLCRJInhHRiUiIiQiIiItSSRjb3NHRik2IywkRi4iIiNGMA==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">dY:=diff(Y,x);   #Here we compute y' and assign the result to dY</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSNkWUc2IiwmKiYtSSRleHBHNiRJKnByb3RlY3RlZEdGK0koX3N5c2xpYkdGJTYjLCRJInhHRiUiIiQiIiItSSRjb3NHRio2IywkRi8iIiNGMUYwKiZGKEYxLUkkc2luR0YqRjRGMSEiIw==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">d2Y:=diff(Y,x$2);  #Note how we write the second derivative!</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSRkMllHNiIsJiomLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRitJKF9zeXNsaWJHRiU2IywkSSJ4R0YlIiIkIiIiLUkkY29zR0YqNiMsJEYvIiIjRjEiIiYqJkYoRjEtSSRzaW5HRipGNEYxISM3</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">d2Y-6*dY+13*Y;  #This is the differential equation- See that it equals zero</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiMiIiE=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"/></Input></Group><Text-field/></Worksheet>