Solve the following stiff initial-value problems using Euler's method, and compare the results with the actual solution.
a. y' = −5y + 6et, 0≤ t ≤ 1, y(0) = 2, with h = 0.1; actual solution y(t) = e−5t + et .
b. y' = −10y+10t+1, 0 ≤ t ≤ 1, y(0) = e, with h = 0.1; actual solution y(t) = e−10t+1+t.
c. y' = −15(y − t−3) − 3/t4, 1 ≤ t ≤ 3, y(1) = 0, with h = 0.25; actual solution y(t) = −e−15t + t−3.
d. y' = −20y + 20 cost − sint, 0 ≤ t ≤ 2, y(0) =0, with h = 0.25; actual solution y(t) = −e−20t + cos t.