Chapter 4.7, Problem 6E

In Problems 5 through 8, determine whether Theorem 5 applies. If it does, then discuss what conclusions can be drawn. If it does not, explain why.

6. y″ + yy′ = t² − 1; y(0) = 1, y′(0) = −1

Existence and Uniqueness of Solutions

Theorem 5. If p(t), q(t), and g(t) are continuous on an interval (a, b) that contains the point t₀, then for any choice of the initial values Y₀ and Y₁, there exists a unique solution y(t) on the same interval (a, b) to the initial value problem

(4) y″(t)     + p(t)y′(t) + q(t)y(t) = g(t); y(t₀) = Y₀, y′(t₀) = Y₁.