[Partial Differential Equations] [PDE] I have 5 questions that I need help with.

May 2018
1
0
US
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These are 5 questions that I need help with. I have access to the solutions but some parts are missing and I can't seem to follow them. I would be very thankful if someone is able to help.

I know that for the first one we need to use the method that involves an equilibrium solution. For the second one, we rely on the Fourier transform (I get this for the most part). For the fourth and fifth, we use the method of separation of variables. While the general approach isn't impossibly hard, I seem to hit roadblocks where there are gaps in the solution. Thanks!
 

Walagaster

MHF Helper
Apr 2018
223
144
Tempe, AZ
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https://d2vlcm61l7u1fs.cloudfront.net/media/4bc/4bc3188a-8b7b-488b-b12f-68363e633986/image

https://d2vlcm61l7u1fs.cloudfront.net/media/c05/c051bba3-9372-4623-99cb-2f47c4e292a3/phpM2xBDI.png

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https://d2vlcm61l7u1fs.cloudfront.net/media/5bc/5bc56a5a-4ea1-4861-be7f-5082ba5a7e11/phpwpJ9pD.png

These are 5 questions that I need help with. I have access to the solutions but some parts are missing and I can't seem to follow them. I would be very thankful if someone is able to help.

I know that for the first one we need to use the method that involves an equilibrium solution. For the second one, we rely on the Fourier transform (I get this for the most part). For the fourth and fifth, we use the method of separation of variables. While the general approach isn't impossibly hard, I seem to hit roadblocks where there are gaps in the solution. Thanks!
I have several suggestions for you.
1. Post these as separate posts.
2. Upload the images to the forum instead of using links.
3. Show us some work on each one so we can see where your difficulty is.

You can't expect anyone to just work all of them and post the solutions here.
 
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