Question: substitute function in PDEs

Dear all

I have a PDEs depend on u1(r,z) 
I would like to decompose u1 as sum of two function c1*r*U(z)+u(r,z) and  , where c1 is constant,  then i would like to substitute u1 in the pde by   c1*r*U(z)+u(r,z) then obtain the corresponding new equation

thank you 

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