MHB Problem 13 from section 16.1 of Taylor's PDE textbook.

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The discussion centers on Problem 13 from section 16.1 of Taylor's PDE textbook, which the poster struggled to solve to their teacher's satisfaction. They provided a link to the problem and attached their unsuccessful attempt along with the teacher's feedback. The poster expresses a desire for assistance in solving the problem, indicating that it was intended to be part of their thesis. They also mention difficulties in uploading attachments to the forum due to file size limitations. The request for help highlights the challenges faced in mastering PDE concepts and the aspiration to complete their MSc.
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I was given as a task to solve this question by my teacher (heck if I had the time I would have solved every problem in both Taylor's and Evans's books on PDE); but didn't succeed to the teacher's satisfaction.

In the following link there's a presentation of the problem, and in the attachment my failed attempt at solving it (it should have been part of my thesis I guess :-( ):
https://math.stackexchange.com/questions/1180968/question-13-in-taylors-pde-vol-iii-section-16-1

Any help on how to solve this?
In the attachment there's the latex file with the remarks my teacher gave me. (His remarks are between the two lines with*******).

Perhaps one day I'll get my MSc...
Taylor_Exercises-new

I tried to upload as an attachment through the option in the MHB forum but didn't succeed as the txt file exceeds the site's capacity, so I uploaded to mediafire.

Thanks in advance for your time!
 
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