Question: Consider the initial value problem
y' = 5 - y, y(0) = 1
(a) Use Euler's method with five steps to estimate y(1).
(b) Sketch the slope field for this differential equation in the first quadrant, and use it to decide if your estimate is an over- or underestimate.
(c) Find the exact solution to the differential equation and hence find y(1) exactly.
(d) Without doing the calculation, roughly what would you expect the approximation for y(1) to be with ten steps?