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814 Answers to Selected Problems

TABLE A.3 Euler Approximations in Problem 5, Section 5.2

x y app (x k ) y(x k )
1 –2 –2
1.05 –2.127015115 –2.129163318
1.10 –2.258244233 –2.262726023
1.15 –2.393836450 –2.400852694
1.20 –2.533952645 –2.543722054
1.25 –2.678768165 –2.691527843
1.30 –2.828472691 –2.844479697
1.35 –2.983271267 –3.002804084
1.40 –3.143385165 –3.166745253
1.45 –3.309052780 –3.336566227
1.50 –3.480530557 –3.512549830

TABLE A.4 Runge-Kutta Approximation in Problem 1, Section 5.3
x y k

0.0 2
0.2 2.16257799
0.4 2.27783452
0.6 2.34198641
0.8 2.35938954
1.0 2.33750216
1.2 2.28392071
1.4 2.20519759
1.6 2.106598
1.8 2.99222519
2.0 2.8652422

TABLE A.5 Runge-Kutta Approximation in Problem 3, Section 5.3

x y k
0 1
0.2 1.26466198
0.4 1.45391187
0.6 1.58485267
0.8 1.67218108
1.0 1.7274517
1.2 1.75945615
1.4 1.77481079
1.6 1.7784748
1.8 1.77415235
2.0 1.76459409

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October 14, 2010 17:50 THM/NEIL Page-814 27410_25_Ans_p801-866