These problem are also due in two days. I just wanted to post them separately because they're two different subjects.Thanks.

1) Apply Euler's Method with h=0.1 to approximate the solution of the initial value problem ==> y'= y- x- 1, y(o)=1 <=== on the interval [0, 1/2]

2) Apply Euler's Method with h=0.25 to approximate the solution of the initial value problem ==> y'=y- x- 1, y(0)=1 <=== on the interval [0, 1/2]

3) Given the initial value problem: dy/dx= y, y(0)= 1. Do the following:

a. Solve the initial value problem and show that e= y(1).

b. Apply Euler's Method with h= 0.25 to approximate e= y(1).

c. Apply improved Euler's Method with h=0.5 to approximate e=y(1).

d. Apply Runge-Kutta Method with h=1 to approximate e= y(1).

e. Find errors of the above approximations of e. Wich approximation is the best?