Example 3.  Show that the systems in examples 1 and 2 are equivalent.  The system  
        [Graphics:Images/NewtonSystemMod_gr_274.gif]  
is equivalent to the system  
        [Graphics:Images/NewtonSystemMod_gr_275.gif]  

Solution 3.

You can do this by hand or you can try a Mathematica derivation.  

Change the second equation.  

[Graphics:../Images/NewtonSystemMod_gr_276.gif]


[Graphics:../Images/NewtonSystemMod_gr_277.gif]


[Graphics:../Images/NewtonSystemMod_gr_278.gif]

[Graphics:../Images/NewtonSystemMod_gr_279.gif]


[Graphics:../Images/NewtonSystemMod_gr_280.gif]

[Graphics:../Images/NewtonSystemMod_gr_281.gif]

Change the second equation.  

[Graphics:../Images/NewtonSystemMod_gr_282.gif]

[Graphics:../Images/NewtonSystemMod_gr_283.gif]


[Graphics:../Images/NewtonSystemMod_gr_284.gif]

[Graphics:../Images/NewtonSystemMod_gr_285.gif]


[Graphics:../Images/NewtonSystemMod_gr_286.gif]

[Graphics:../Images/NewtonSystemMod_gr_287.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004