SECTION 5.5 Differential Equations 315
We can tabulate the results:
n xn yn=yn− 1 n xn yn=yn− 1
+F(xn− 1 ,yn− 1 ) +F(xn− 1 ,yn− 1 )h
0 0 1 6 1.2 1.788
1 .2 1 7 1.4 2.1832
2 .4 1.04 8 1.6 2.6998
3 .6 1.128 9 1.8 3.3598
4 .8 1.2736 10 2.0 4.1917
5 1.0 1.4883The figure below compares the exact solution with the approxima-
tions generated above.
Exercises
- Give the exact solution ofy′=x+y− 1 , y(0) = 1. Tabulate these
exact values against their approximations in the table below: