Example 12.22.  Show that  [Graphics:Images/LaplaceMultDivMod_gr_27.gif].

Explore Solution 12.22.

Use the fact that  [Graphics:../Images/LaplaceMultDivMod_gr_33.gif].
Use Theorem 12.18 and find  [Graphics:../Images/LaplaceMultDivMod_gr_34.gif].

[Graphics:../Images/LaplaceMultDivMod_gr_35.gif]




[Graphics:../Images/LaplaceMultDivMod_gr_36.gif]

 

 

 

 

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

[Graphics:../Images/LaplaceMultDivMod_gr_37.gif]





[Graphics:../Images/LaplaceMultDivMod_gr_38.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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