316 CHAPTER 5 Series and Differential Equations
n xn yn=yn− 1 +F(xn− 1 ,yn− 1 )h y(xn)
0 0 1
1 .2 1
2 .4 1.04
3 .6 1.128
4 .8 1.2736
5 1.0 1.4883
6 1.2 1.788
7 1.4 2.1832
8 1.6 2.6998
9 1.8 3.3598
10 2.0 4.1917- Use the Euler method withh= 0.1 to find approximate values for
the solution of the initial-value problem over the interval [1,2]
xy′+y= 3x^2 , y(1) =− 2.Then solve exactly and compare against the approximations.- Do the same over the interval [0,1], (h= 0.1) for
y′= 2xy+1
y, y(0) = 1.