Elliptic Canonical Form

• May 25th 2011, 08:05 AM
Alexrey
Elliptic Canonical Form
Hey guys, I've been doing some elliptic 2nd order PDE problems in my book and I'm having a little trouble. This is the question:

Determine the canonical form of: Uxx + 2Uxy + 5Uyy + Uy = 0 (i.e. u sub xx, u sub xy etc.)

I've done this thing like 3 times now and always come to an answer that is different from the answer in my book. I got the following canonical form:

Wss + Wtt + (1/8)Wt = 0 (i.e. w sub ss, w sub tt etc.) but the book got Wss + Wtt + (1/8)Ws + (1/8)Wt = 0

Surely the book is wrong? I followed everything to the letter and still managed to get a different answer.
• May 25th 2011, 08:33 AM
Alexrey
Aha, wait I see that you want a canonical form with A=C, that's where I went wrong. This thread can be closed, sorry!
• May 25th 2011, 08:34 AM
Ackbeet
You can mark your thread as solved by using the Thread Tools -> Mark this Thread as Solved... option. We don't normally close threads just because they're solved; at least not here on MHF. Takes too much time and it's not worth it.