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Help: How to solve PDE in Mathematica?



Dear group, 

Could you tell me who to get the general analytical solution of the following function

1. Uxy - Uy = 0

2.  U + 2 Ux + 2 Uy +4 Uxy = 0


U is function of x and y.  

Something strange is:  although I can calculate the general solution by hand for the first equation easily, I can't use mathematica to get the solution.  

I have tried two ways:

  ~ the DSolve   and 

  ~ the following way

<<Calculus`DSolveIntegrals`

CompleteIntegral[Derivative[1, 1][u][x, y] - Derivative[0, 1][u][x, y] == 0, 
  u[x, y], {x, y}]


Thanks a lot!

Li



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