🧮 Exploring Problem 1.2.3 from Zill – Nonlinear IVP with Domain Analysis

“Understanding where a function is defined is as important as knowing what it looks like.” – Me, solving ODEs on a Sunday ☕📘

📌 Problem Overview

In today’s post, I’m working through Problem 1.2.3 from Advanced Engineering Mathematics by Dennis Zill. This one is a nice change of pace: we not only find a particular solution to a first-order differential equation, but also identify the largest interval over which that solution is valid.

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✍️ Step-by-Step Solution

Let’s solve this systematically:

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