Given the initial-value problem

y' = 1/t² – y/t − y², 1≤ t ≤ 2, y(1) = −1,

With exact solution y(t) = −1/t:

a. Use Euler’s method with h = 0.05 to approximate the solution, and compare it with the actual values of y.

b. Use the answers generated in part (a) and linear interpolation to approximate the following values of y, and compare them to the actual values.

i. y(1.052) 

ii. y(1.555) 

iii. y(1.978)

c. Compute the value of h necessary for | y(t_i) − w_i| ≤ 0.05 using Eq. (5.10).