Module 4: Systems of Equations and Equations of Order Greater Than One
Lecture 13: Direct Methods For Higher Order Equations
Substituting (4.7) into (4.6), we get
(4.8)
If and , (4.8) will agree with the first four terms of the Taylor's series expansion of . The term in will not match the fifth term in the Taylor's series for any choice of and . Similarly, if and then agrees with to order . Thus, one solution is
and 
, (4.8) will agree with the first four terms of the Taylor's series expansion of 
. The term in 
will not match the fifth term in the Taylor's series for any choice of 
and 
. Similarly, if 
and 
then 
agrees with 
to order 
. Thus, one solution is 
