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How would you go about finding which of the following PDEs can be separated into ODEs...

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Advance Math

How would you go about finding which of the following PDEs canbe separated into ODEs by assuming a product of unknown functionsx,y, and z?

1) aUxy+bU=0

2) x^2Uxx+yUyy=0

3) Uxx+3Uxy+7Uy=0

4)Uxx+Uyy+Ux+Uy=0

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