Example 12.9.  Show that  [Graphics:Images/LaplaceTransformMod_gr_121.gif].  

Explore Solution 12.9.

Since  [Graphics:../Images/LaplaceTransformMod_gr_125.gif],  we can apply the results of Example 12.8;   [Graphics:../Images/LaplaceTransformMod_gr_126.gif].  

[Graphics:../Images/LaplaceTransformMod_gr_127.gif]





[Graphics:../Images/LaplaceTransformMod_gr_128.gif]
[Graphics:../Images/LaplaceTransformMod_gr_129.gif]
[Graphics:../Images/LaplaceTransformMod_gr_130.gif]
[Graphics:../Images/LaplaceTransformMod_gr_131.gif]
[Graphics:../Images/LaplaceTransformMod_gr_132.gif]
[Graphics:../Images/LaplaceTransformMod_gr_133.gif]
[Graphics:../Images/LaplaceTransformMod_gr_134.gif]
[Graphics:../Images/LaplaceTransformMod_gr_135.gif]
[Graphics:../Images/LaplaceTransformMod_gr_136.gif]
[Graphics:../Images/LaplaceTransformMod_gr_137.gif]
[Graphics:../Images/LaplaceTransformMod_gr_138.gif]
[Graphics:../Images/LaplaceTransformMod_gr_139.gif]
[Graphics:../Images/LaplaceTransformMod_gr_140.gif]



Aside. We can check this with Mathematica's  result using the LaplaceTransform package.

[Graphics:../Images/LaplaceTransformMod_gr_141.gif]




[Graphics:../Images/LaplaceTransformMod_gr_142.gif]
[Graphics:../Images/LaplaceTransformMod_gr_143.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2006 John H. Mathews, Russell W. Howell