Page 375 - Schaum's Outline of Differential Equations

358 A ANSWERS TO SUPPLEMENTARY PROBLEMS

18.35. Method: EULER'S METHOD

Problem: / = -y + x + 2; y(0) = 2
y
x n n True solution
x
ft = 0.1 h = 0.05 ft = 0.01 Y(x) = e~ + x+l
0.0 2.0000 2.0000 2.0000 2.0000

0.1 2.0000 2.0025 2.0044 2.0048
0.2 2.0100 2.0145 2.0179 2.0187
0.3 2.0290 2.0351 2.0397 2.0408

0.4 2.0561 2.0634 2.0690 2.0703

0.5 2.0905 2.0987 2.1050 2.1065
0.6 2.1314 2.1404 2.1472 2.1488
0.7 2.1783 2.1877 2.1948 2.1966

0.8 2.2305 2.2401 2.2475 2.2493

0.9 2.2874 2.2972 2.3047 2.3066
1.0 2.3487 2.3585 2.3660 2.3679

18.36. Method: EULER'S METHOD

2
Problem: y' = 4x ; y(0) = 0
y
x n n True solution
h = 0.l h = 0.05 ft = 0.01 Y(x) = x 4
0.0 0.0000 0.0000 0.0000 0.0000

0.1 0.0000 0.0000 0.0001 0.0001
0.2 0.0004 0.0009 0.0014 0.0016

0.3 0.0036 0.0056 0.0076 0.0081
0.4 0.0144 0.0196 0.0243 0.0256

0.5 0.0400 0.0506 0.0600 0.0625
0.6 0.0900 0.1089 0.1253 0.1296

0.7 0.1764 0.2070 0.2333 0.2401
0.8 0.3136 0.3600 0.3994 0.4096

0.9 0.5184 0.5852 0.6416 0.6561
1.0 0.8100 0.9025 0.9801 1.0000