The solutions is

Should this be set equal to

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- January 9th 2011, 03:14 PMdwsmithDE Change of Variables

The solutions is

Should this be set equal to - January 9th 2011, 09:00 PMdwsmith

Let D = 0 and B = 1 since y = 0, both D and B are arbitrary, and .

This is obviously wrong but I don't know what to do differently. - January 10th 2011, 08:05 AMJester
You got two things going on that seems to be confusing you - (1) a rotation of coordinates and (2) a general change of coordinates. Let me see if I can help.

Your problem is

You have introduced a linear change of variables (this can be more general but it's not necessary here)

.

What you want is to transform your PDE to essentially an ODE by choosing the constant and with the requirement that (why?).

As you've said

and picked and (that's good!) so

.

You still have the flexibility to choose and anything. You further chose and so

.

This is also good b/c the boundary

.

Now you must switch everthing over in terms of your new variables so since

then your new problem is

with when .

Now follow what you did in post #2. - January 10th 2011, 01:06 PMdwsmith
- January 10th 2011, 01:37 PMJester
The right hand side is

From your change of variables

so

.