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

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Advance Math

How would you do the work to find which PDEs below can beseparated into ODEs by assuming a product of unknown functions x,yand z?

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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