Suppose that we use Euler's method to approximate the solution to the differential equation dy x y(0.4) = 1. =-; dx y Letf(x, y) -x1/y We let xo 0.4 and yo 1 and pick a step size h- 0.2. Euler's method is the the following algorithm. Fromxn and yn, our approximations to the solution of the differential equation at the nth stage, we find the next stage by computing xn+1-xn + ?, ??+,-?, + h .fon,%). Complete the following table:
yn 0 0.4 1.08 1.22814 4 1.2 5 1.4
The exact solution can also be found using separation of variables. It is
y(a)=
Thus the actual value of the function at the point
x 1.4=