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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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Transcribed Image Text:(a) Given a differential equation r'x +2rx -tx +x= 122. Show that x=÷+cx+c3tlnt +4r? is a solution of the the differential equation. Assume an appropriate interval/ of definition. Given a differential equation x = (zx) that passes through a point (fo, xo). (b) determine a region of the rx-plane for which the differential equation would have a unique solution. (c) In an experiment, a test tube containing a chemical is immersed in a water bath. At = 0, the temperature, H (t) of the chemical in the test tube is 27°C. The controlled temperature (measured in degrees Celcius) of the water bath is H„ (1) = 38 –22e",1>0, where r is measured in minutes. Referring to the Newton's empirical law -k(H-H,.), where k is the proportionality constant assumed to be -0.1 per minute, answer the following questions: In words, discuss the profile of the temperature H (1) in the shord term AND in the long term (Calculation is not needed). () (i) Solve this initial value problem.

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