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ClearAll[u,u0,t,z,L0];
pde=D[u[z,t],t]== D[u[z,t],{z,2}];
bc={u[0,t]==0,u[L0,t]==0}
ic=u[z,0]==u0
NumericQ[L0]=True;
sol=DSolve[{pde,bc,ic},u[z,t],{z,t}]
% /. L0 -> 2
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