# Discussion. 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.

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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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Step 1

We need to find the interval of validity for the initial value problem given below.

Step 2

Divide the coefficient of derivative to change the given equation to the general form,

Step 3

By comparing this equation wit...

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