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How would you do the work to find which PDEs below can be separated into ODEs...

How would you do the work to find which PDEs below can be separated into ODEs by assuming a product of unknown functions x,y and z? Please be very detailed

1) Uxx+Uyy+Uzz=0

2) Uxx+Uyy+Ux+Uy=0

3) Uxx+3Uxy+Uyy=0

4) Uxx+3Uxy+7Uy=0

5) x^2Uxx+yUyy=0

6) aUxy+bu=0

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