Example 5. Solve with over .
Solution 5.
Just for fun, plot both the Euler solution and the modified Euler solution. Notice that there is a difference.
(c) John H. Mathews 2004
![[Graphics:Images/Euler'sMethodMod_gr_114.gif]](../Images/Euler'sMethodMod_gr_114.gif){kind=small}
with ![[Graphics:Images/Euler'sMethodMod_gr_115.gif]](../Images/Euler'sMethodMod_gr_115.gif){kind=small}
over ![[Graphics:Images/Euler'sMethodMod_gr_116.gif]](../Images/Euler'sMethodMod_gr_116.gif){kind=small}
. with over .![[Graphics:../Images/Euler'sMethodMod_gr_117.gif]](../Images/Euler'sMethodMod_gr_117.gif)
![[Graphics:../Images/Euler'sMethodMod_gr_118.gif]](../Images/Euler'sMethodMod_gr_118.gif)
![[Graphics:../Images/Euler'sMethodMod_gr_125.gif]](../Images/Euler'sMethodMod_gr_125.gif)
![[Graphics:../Images/Euler'sMethodMod_gr_119.gif]](../Images/Euler'sMethodMod_gr_119.gif){kind=small}
![[Graphics:../Images/Euler'sMethodMod_gr_120.gif]](../Images/Euler'sMethodMod_gr_120.gif){kind=small}
![[Graphics:../Images/Euler'sMethodMod_gr_121.gif]](../Images/Euler'sMethodMod_gr_121.gif)
![[Graphics:../Images/Euler'sMethodMod_gr_122.gif]](../Images/Euler'sMethodMod_gr_122.gif){kind=small}
![[Graphics:../Images/Euler'sMethodMod_gr_123.gif]](../Images/Euler'sMethodMod_gr_123.gif){kind=small}
![[Graphics:../Images/Euler'sMethodMod_gr_124.gif]](../Images/Euler'sMethodMod_gr_124.gif)
![[Graphics:../Images/Euler'sMethodMod_gr_126.gif]](../Images/Euler'sMethodMod_gr_126.gif){kind=small}
![[Graphics:../Images/Euler'sMethodMod_gr_127.gif]](../Images/Euler'sMethodMod_gr_127.gif){kind=small}
![[Graphics:../Images/Euler'sMethodMod_gr_128.gif]](../Images/Euler'sMethodMod_gr_128.gif)
![[Graphics:../Images/Euler'sMethodMod_gr_129.gif]](../Images/Euler'sMethodMod_gr_129.gif){kind=small}
![[Graphics:../Images/Euler'sMethodMod_gr_130.gif]](../Images/Euler'sMethodMod_gr_130.gif){kind=small}
![[Graphics:../Images/Euler'sMethodMod_gr_131.gif]](../Images/Euler'sMethodMod_gr_131.gif)
![[Graphics:../Images/Euler'sMethodMod_gr_132.gif]](../Images/Euler'sMethodMod_gr_132.gif)
![[Graphics:../Images/Euler'sMethodMod_gr_133.gif]](../Images/Euler'sMethodMod_gr_133.gif){kind=small}