5. Use Taylor's method of order two to approximate the solution for each of the following initial-value problems.
a. \( \quad y^{\prime}=y / t-(y / t)^{2}, \quad 1 \leq t \leq 1.2, \quad y(1)=1 \), with \( h=0.1 \)
b. \( \quad y^{\prime}=\sin t+e^{-t}, \quad 0 \leq t \leq 1, \quad y(0)=0 \), with \( h=0.5 \)
c. \( \quad y^{\prime}=\left(y^{2}+y\right) / t, \quad 1 \leq t \leq 3, \quad y(1)=-2 \), with \( h=0.5 \)
d. \( \quad y^{\prime}=-t y+4 t y^{-1}, \quad 0 \leq t \leq 1, \quad y(0)=1 \), with \( h=0.25 \)