Use Euler's Method to compute y(4) given that y' = y - x^2 , y(1)

Question.

Consider the initial value problem y'= y - x², y(1) = 2.

(a) For this IVP, write down Euler's method for y_n+1 in terms of y_n for a general stepsize h.

(b) Using one step of Euler's method approximate y(4).

(c) Using three steps of Euler's method approximate y(4).

Solution: