Transforming a PDE with Laplace method

[SeM]

Hello, I have the following PDE equation:

a*b/U(u)*V(v) = 0

where a and b are arbitrary constants, and U an V are two unknown functions. To me it appears this has no solution, however I would like to ask if anyone has some suggestions, such as transforming it to another type using Fourier or Laplace transform.

Thanks

 

[Orodruin]

How is that a PDE?

The obvious solution would be that $b = 0$ or $a = 0$.

It sounds like this is part of a larger problem. You might want to post the problem in the homework section, stating the entire problem formulation and showing your own work to arrive to that equation.

 

[SeM]

It is part of the given PDE:

$$ r^2 \frac{1}{R}\frac{\partial^2 R}{\partial r^2} - (r+2i r^2) \frac{1}{R}\frac{\partial R}{\partial r} - \frac{r^2}{RY} = \frac{1}{Y} \frac{\partial^2 Y}{\partial \theta^2}+2ir \frac{1}{Y}\frac{\partial Y}{\partial \theta}$$

and I am not really sure how to consider it.