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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A: Solution:

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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 differential equations.