The actual solutions to the initial$-$value problems in Exercise $1$ are given here. Compare the actual error at each step to the error bound.

a$.,y(t)=\frac{1}{5}t{e}^{3t}-\frac{1}{25}{e}^{3t}+\frac{1}{25}{e}^{-2t}$

b$.,y(t)=t+\frac{1}{1-t}$

c$.,y(t)=tlnt+2t$

d$.,y(t)=\frac{1}{2}sin2t-\frac{1}{3}cos3t+\frac{4}{3}$