The actual solutions to the initial$-$value problems in Exercise $2$ are given here. Compute the actual error and compare this to the error bound if Theorem $5\mathrm{.}9$ can be applied.

a$.,y(t)=ln(e^t+e-1)$

b$.y(t)=\sqrt[\phantom{2}]{t^2+2t+6}-1$

c$.,y(t)=(t-2+\sqrt[\phantom{2}]{2}e{e}^{-\frac{t}{2}}{)}^2$

d$.y(t)=\frac{4+cos2-cos2t}{2t^2}$