Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN: 9781133382119
Author: Swokowski
Publisher: Cengage
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Differential Equations
Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…
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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