<?xml version="1.0" encoding="utf-8" ?>
<problist>
  <prob>
     <name>Unheated building (Zill 1.3 #6)</name>
     <flags>0</flags>
     <dydx>-0.1*(y-F(x))</dydx>
     <x>0,96,24</x>
     <y>40,120,23</y>
     <method>euler</method>
     <h>0.1</h>
     <points>
     	<point>[0,100]</point>
     </points>
     <expr>F(x)=80-30cos(pi x/12);color=purple</expr>
  </prob>
  <prob>
     <name>Circle</name>
     <fn>-x/y</fn>
     <x>-3,3,24</x>
     <y>-2,2,16</y>
     <method>rk4,true,0.05</method>
     <points>
     	<point>[0,1]</point>
     	<point>[1,1]</point>
     	<point>[2,0]</point>
     </points>
  </prob>
  <prob>
     <name>Undamped pendulum</name>
     <fn>-sin(x)/y</fn>
     <x>-2pi,2pi,24</x>
     <y>-4,4,16</y>
     <method>rk4,true,0.05</method>
     <points>
     	<point>[0,-3]</point>
     	<point>[0,2.2]</point>
     	<point>[0,1]</point>
     	<point>[0,2]</point>
     	<point>[0,-2]</point>
     </points>
  </prob>
  <prob>
     <name>Undamped pendulum (system)</name>
     <flags>2</flags>
     <SYS>t,y,v</SYS>
     <dydx>-sin(x)/y</dydx>
     <dxdt>v</dxdt>
     <dydt>-sin(y)</dydt>
     <x>-2pi,2pi,24</x>
     <y>-4,4,16</y>
     <method>rk4</method>
     <h>0.05</h>
     <points>
     	<point>[0,2]</point>
     	<point>[0,1]</point>
     	<point>[0,-3]</point>
     	<point>[0,2.2]</point>
     	<point>[0,-2]</point>
     </points>
	 <expr>y^2=A+2cos(x);color=black</expr>
  </prob>
  <prob>
     <name>Damped pendulum</name>
	 <fn>-0.5-sin(x)/y</fn>
     <x>-pi,3pi,24</x>
     <y>-4,4,16</y>
     <method>rk4,true,0.01</method>
     <points>
     	<point>[0,2]</point>
     	<point>[0,-2]</point>
     	<point>[2,2]</point>
     	<point>[0,1]</point>
     </points>
  </prob>
  <prob>
     <name>Damped pendulum (system)</name>
     <flags>2</flags>
     <SYS>t,y,v</SYS>
     <dydx>-0.5-sin(x)/y</dydx>
     <dxdt>v</dxdt>
     <dydt>-0.5v-sin(y)</dydt>
     <x>-pi,3pi,24</x>
     <y>-4,4,16</y>
     <method>rk4</method>
     <h>0.01</h>
     <points>
     	<point>[0,2]</point>
     	<point>[0,-2]</point>
     	<point>[2,2]</point>
     	<point>[0,1]</point>
     </points>
  </prob>
  <prob>
     <name>Predator-prey</name>
     <fn>y/x*(.005x-0.2)/(0.4-0.05y)</fn>
     <x>0,100,15</x>
     <y>0,16,15</y>
     <method>rk4,true,0.09</method>
     <points>
     	<point>[80,9]</point>
     	<point>[20,4]</point>
     </points>
  </prob>
  <prob>
     <name>Predator-prey (system)</name>
	 <flags>2</flags>
     <SYS>t,r,f</SYS>
	 <dydx>y/x*(.005x-0.2)/(0.4-0.05y)</dydx>
     <dxdt>r*(0.4-0.05f)</dxdt>
     <dydt>f*(.005r-0.2)</dydt>
     <x>0,100,15</x>
     <y>0,16,15</y>
     <method>rk4</method>
     <h>0.1</h>
     <points>
     	<point>[80,9]</point>
     	<point>[20,4]</point>
     </points>
  </prob>
  <prob>
     <name>Beetles on a square</name>
     <fn>(y-x)/(x+y)</fn>
     <x>-3,3,21</x>
     <y>-2,2,15</y>
     <method>rk4,true,0.04</method>
     <points>
     	<point>[1,1]</point>
     	<point>[0,1]</point>
     	<point>[-1,0]</point>
     </points>
  </prob>
  <prob>
     <name>Beetles on a square (system)</name>
     <flags>2</flags>
     <dydx>(y-x)/(x+y)</dydx>
     <dxdt>-x-y</dxdt>
     <dydt>x-y</dydt>
     <x>-3,3,21</x>
     <y>-2,2,15</y>
     <method>rk4</method>
     <h>0.04</h>
     <points>
     	<point>[1,1]</point>
     	<point>[0,1]</point>
     	<point>[-1,0]</point>
     </points>
	 <expr>r=5e^-@;color=black;amax=4pi</expr>
  </prob>
  <prob>
     <name>BDH 1.3 #1</name>
     <fn>x^2+x</fn>
     <x>-3,3,15</x>
     <y>-2,2,15</y>
     <method>euler,false,0.1</method>
  </prob>
  <prob>
     <name>BDH 1.3 #2</name>
     <fn>1-2y</fn>
     <x>-3,3,15</x>
     <y>-2,2,15</y>
     <method>euler,false,0.1</method>
  </prob>
  <prob>
     <name>BDH 1.3 #3</name>
     <fn>y+x+1</fn>
     <x>-3,3,15</x>
     <y>-2,2,15</y>
     <method>euler,false,0.1</method>
  </prob>
  <prob>
     <name>BDH 1.3 #4</name>
     <fn>x^2+1</fn>
     <x>-3,3,15</x>
     <y>-2,2,15</y>
     <method>euler,false,0.1</method>
  </prob>
  <prob>
     <name>BDH 1.3 #5</name>
     <fn>2y*(1-y)</fn>
     <x>-3,3,15</x>
     <y>-2,2,15</y>
     <method>euler,false,0.1</method>
  </prob>
  <prob>
     <name>BDH 1.3 #6</name>
     <fn>4y^2</fn>
     <x>-3,3,15</x>
     <y>-2,2,15</y>
     <method>euler,false,0.1</method>
  </prob>
  <prob>
     <name>BDH 1.3 #12</name>
     <fn>y(y-1)(y-1)</fn>
     <x>-3,3,15</x>
     <y>-2,2,15</y>
     <method>euler,false,0.1</method>
  </prob>
  <prob>
     <name>BDH 1.4 #1</name>
     <fn>2y+1</fn>
     <x>0,2,15</x>
     <y>0,60,15</y>
     <method>euler,false,0.5</method>
     <points>
     	<point>[0,3]</point>
     </points>
  </prob>
  <prob>
     <name>BDH 1.4 #2</name>
     <fn>x-y^2</fn>
     <x>0,2,15</x>
     <y>0,2,15</y>
     <method>euler,false,0.5</method>
     <points>
     	<point>[0,1]</point>
     </points>
  </prob>  <prob>
     <name>BDH 2.1 #7</name>
	 <flags>2</flags>
     <SYS>t,r,f</SYS>
	 <dydx>y/x*(.005x-0.2)/(0.4-0.05y)</dydx>
     <dxdt>2(1 - r/3)r - r*f</dxdt>
     <dydt>-2f + 4r*f</dydt>
     <x>0,1.5,15</x>
     <y>0,4,15</y>
     <method>rk4</method>
     <h>0.05</h>
     <points>
     	<point>[1,0.3]</point>
     </points>
  </prob>
</problist>