**Use Euler’s method to approximate y(0.2), where y(x) is the solution of the initial-value problem y”-(2x + 1)y =1, y(0)=3, y'(0) ?=1. First use one step with h =0.2 and then repeat the calculations using two steps with h =0.1.**

we shall rewrite this equation as folllows:

we then let

thus

the recursive euler’s method is

starting with h=0.2;

thus

then h=0.1;

also

then