APM346-2012 > Home Assignment 1

Problem 2

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Peishan Wang:
Could you give some hints to Q2? There's no way that I can make the general solution continuous at (0,0)..... Thanks a lot!

Victor Ivrii:
First, I need to apologize: this problem contained a misprint which I just corrected. The source of errors is simple: everything was done in the extreme rush and nobody checked it.

Now hint: it may happen in some problems that the solution (having certain properties) does not exist or must have a very special form. Then the your presented solution should state this.

I am not claiming that this is the case with this problem but your statement is wrong anyway: there is at least one continuous solution $u=0$ identically.

Peishan Wang:
Thank you for your hint but I still didn't get the point..

For example if the general solution has the form f(x/y), how can I make them continuous at (0,0)? Thanks!!

Victor Ivrii:

--- Quote from: Peishan Wang on September 21, 2012, 07:19:46 PM ---Thank you for your hint but I still didn't get the point..

For example if the general solution has the form $f(x/y)$, how can I make it continuous at (0,0)? Thanks!!

--- End quote ---

You are almost done (but check the general solutions!) Think - and don't post solutions!!!

Fatima Yousuf:
Hi, for number 2, say we get $u = f(g(x,y))$ for our general solution when $(x,y) \ne (0,0)$. Then are we just finding a $u(0,0)$ that is equal to the limit of $u = f(g(x,y))$ as $(x,y)$ approaching $(0,0)$ in order to make u continuous at $(0,0)$?

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