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(b) Here are graphs of solutions of the above equation on [0, T]. While most solutions tend to +∞ or -∞ at zero, there is one solution (graph shown in black) that has a finite limit as x tends to zero Find this solution. Explain why this solution is the only one that has a limit at zero.

(b) Here are graphs of solutions of the above equation on [0, T]. While most solutions tend to +∞ or -∞ at zero, there is one solution (graph shown in black) that has a finite limit as x tends to zero Find this solution. Explain why this solution is the only one that has a limit at zero.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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How do you do b)?

(a) Find the general solution to the differential equation dy + (cot x) · y = 1. dx (b) Here are graphs of solutions of the above equation on 0, T). While most solutions tend to +0 or -o at zero, there is one solution (graph shown in black) that has a finite limit as x tends to zero. Find this solution. Explain why this solution is the only one that has a limit at zero.
Transcribed Image Text:(a) Find the general solution to the differential equation dy + (cot x) · y = 1. dx (b) Here are graphs of solutions of the above equation on 0, T). While most solutions tend to +0 or -o at zero, there is one solution (graph shown in black) that has a finite limit as x tends to zero. Find this solution. Explain why this solution is the only one that has a limit at zero.
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