Suppose the perturbation (t) is proportional to t, that is, (t) = t for some constant .

Question:

Suppose the perturbation δ(t) is proportional to t, that is, δ(t) = δt for some constant δ. Show directly that the following initial-value problems are well-posed.
a. y' = 1 − y, 0≤ t ≤ 2, y(0) = 0
b. y' = t + y, 0≤ t ≤ 2, y(0) = −1
c. y' = 2/t y + t2et, 1≤ t ≤ 2, y(1) = 0
d. y' = −2/t y + t2et, 1≤ t ≤ 2, y(1) = √2e