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The simplest way is just to use the subs (or substitute) method of your symbolic expression like so:

sage: t = var('t')
sage: uR = function('uR', t)
sage: iL = function('iL', t)
sage: uC = function('uC', t)
sage: 
sage: SE = uR(t) == 3*iL(0) + uC(0)/2 - 4
sage: SE.subs(iL(0)==0)
uR(t) == 1/2*uC(0) - 4
sage: SE.subs(uC(0)==0)
uR(t) == 3*iL(0) - 4
sage: SE
uR(t) == 3*iL(0) + 1/2*uC(0) - 4

You see from the last line that the object SE is not changed during the substitution, so you should assign the result of the substitution. Also, you can do both (or arbitrarily many) substitutions using a dictionary:

sage: R = SE.subs({iL(0):0, uC(0):0})
sage: R
uR(t) == -4