MathAdvanced MathQ&A LibraryDiscussion. Given an initial value problemy′ + p(t)y = q(t), y(t0) = y0 ,the interval of validity is the largest interval that contain t0 and does not containany discontinuity for p(t) or q(t). The existence and uniqueness theorem guaranteesthere is a unique solution on the interval of validity.Problem: Without solving, determine the interval of validity for the initial valueproblem(t2 − 9)y′ + 2y = ln |20 − 4t| , y(4) = −3.

Question

Discussion. Given an initial value problem

y

′ + p(t)y = q(t), y(t0) = y0 ,

the interval of validity is the largest interval that contain t0 and does not contain

any discontinuity for p(t) or q(t). The existence and uniqueness theorem guarantees

there is a unique solution on the interval of validity.

Problem: Without solving, determine the interval of validity for the initial value

problem

(t

2 − 9)y

′ + 2y = ln |20 − 4t| , y(4) = −3.

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