Page 833 - Advanced_Engineering_Mathematics o'neil

Answers to Selected Problems 813

3
2

1
y (x)
0
–3 –2 – 1 0 1 2 3
x
–1
–2

–3

FIGURE A.10 Direction field and solution
for Problem 5, Section 5.1

TABLE A.1 Euler Approximations in Problem 1, Section 5.2
x y app (x k ) y(x k )

0.0 1 1
0.05 1 1.001250521
0.10 1.002498958 1.001250521
0.15 1.007503103 1.005008335
0.20 1.015031072 1.020133420
0.25 1.025113849 1.031575844
0.30 1.037794710 1.045675942
0.35 1.053129175 1.062502832
0.40 1.071184959 1.082138316
0.45 1.092041913 1.104676904
0.50 1.115791943 1.130225803

TABLE A.2 Euler Approximations in Problem 3, Section 5.2
x y app (x k ) y(x k )
0.00 5 5
0.05 5 5.018785200
0.10 5.0375 5.075565325
0.15 5.1130625 5.171629965
0.20 5.228106406 5.309182735
0.25 5.384949598 5.491425700
0.30 7.404305698 5.722683920
0.35 10.73624326 6.008576785
0.40 16.37277097 6.356245750
0.45 26.19643355 6.774651405
0.50 43.87902620 7.274957075

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October 14, 2010 17:50 THM/NEIL Page-813 27410_25_Ans_p801-866