Transforming Partial Differential Equations into Constant Coefficient Form

[Nuel1647]

Homework Statement

The problem statement can be expressed in one of these forms listed in order of preference.

[/B]

Every character with exception of x, y, t, and C are constants.

Homework Equations

I require a change of variable or series of subsequent change of variables that can convert anyone of these equations into an equation having constant coefficients.

The Attempt at a Solution

I have tried x₁=(U₀*beta + x*U_d)
I have also tried d/dx=((U₀*beta/x)+U_d) d/dx₁ and d/dy=y d/dy₁

where x₁ and y₁ are the new variables for x and y respectively.
I know how to do the rest, like changing the boundary conditions and finding an a solution, I just need an appropriate equation for my variable transformation.
Any comment at all (including things like this equation is not solvable and why that is so) regarding the problem will be welcomed.

 

[Chestermiller]

Is phi a function of x and y?

Chet