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BELL SYSTEM TECHNICAL JOURNAL 



Example 4, Fig. 6 



y = -\- xy, ^ X ^ 2 



>;(0) = 1, y(0) = 

 Exact solution: 



y{x) = r(f)3-'^'"/-„3(|/'^). 

 (a) Wave perturbation 

 Wq = cosh X 



X 



Wi = — - cosh X + l{x- — 2:*: + 1) sinh x 



(b) Linear perturbation 



Lo= 1 



Li = 



This is an example in which the exact solution is non-oscillatory yet even 

 in the short interval (0, 2) Wq + Wi is a better approximation than Lo + 



Example 5, Table I 



/' + - y + 3' = 0, < a: ^ oc 



X 



Solution required to match the accurate solution 



y{x) = Jq{x) — i N{i{x) 

 at infinity: 



\\ = ^^= e 

 -Vttx 



