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In the search for a more general recipe, however, we choose to eliminate the first-order derivatives Z $^{′}$( z ), Φ $^{′}$( ϕ ), and R $^{′}$( ρ ). At this point, the elimi- nation of the first-order derivatives of Z ( z ) and Φ ( ϕ ) is achieved through the substitutions 

to imply that 

and 

Whereas, the elimination of the first-order derivative of R ( ρ ) may be sought through the substitutions 

(with the restriction that b is a non-zero constant to avoid triviality) to imply that 

It should be noted here that the choice of g ( ρ ) = bρ 2 υ $^{+1}$/ 2 in (9) is manifestly mandated by the elimination of the first-order derivative of U ( ρ ). 

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