y′ = t, y(0) = 1, solution: y(t) = 1+t2/2
y′ = 2(t + 1)y, y(0) = 1, solution: y(t) = et2+2t
y′ = 5t4y, y(0) = 1, solution: y(t) = et5
y′ = t3/y2, y(0) = 1, solution: y(t) = (3t4/4 + 1)1/3
For the IVPs above, make a log-log plot of the error of Backward
Euler and Implicit Trapezoidal Method, at t = 1 as a function of
hwithh=0.1×2−k for0≤k≤5.