Originally Posted by

**DMDil** Guys, i wanna understand this problem , i don't know how to do this. Please guide me.

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

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

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

3. Apply Improved Euler's method with h = 0.5 to approximate e = y(1).

4. Apply Runge-Kutta method with h = 1 to approximate e = y(1).

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