Consider the differential equation give by

y′ = -10(y - sin t)

(a) Derive by hand exact solution that satis?es the initial condition y(0) = 1.

(b) Numerically obtain the solution to the IVP using Forward Euler with a step size of h = 0.1 from t = 0 to t = 3. Print the value of the approximate solution at time t = 3. Also plot the exact solution (with a solid line) and the approximate solution (with square markers) on the same plot.

(c) Numerically determine the relative global error,

of your approximate solution at t = 3 when h = h, h/2, h/4, h/8 and h/16.

Plot the log of the relative error vs. the log of the spacing h. Explain why this veri?es your scheme is convergent to order 1.