Answer to Question #307743 in Differential Equations for Junior Pyakara

Question

Consider the following initial value problems:

y' =e^(x-y) , x is greater than or equal to Zero or x is less than or equal to one , y(0)=0, h=0.5

actual solution: Y (x) = 1/5 x exp (3x) -1/(25) exp (3x) + 1/25 exp (-2x),

a) Use the Euler method to approximate the solutions of initial-value problem, and compare the results to the actual values

b) Use the Heuns Method to approximate the solutions of initial- value problem, and compare the results to the actual values

C) Use the Runge-Kutta method of order four to approximate the solutions of initial- value problem, and compare the results to the actual values