input resistance of differential amplifier
I think, this question needs - at first - some definitions.

(1) Common mode is clearly defined: Vb1=Vb2

(2) Unsymmetrical diff. mode: Vb1 finite and Vb2=0.

(3) Symmetrical diff. mode: Vb2=-Vb1

(4) General symm. mode: Vb1 finite and Vb2 finite (with Vb1 not equal to Vb2).

Input resstances: For the first three cases, it is a realtively simple task to find the dynamic input resistances rin (here given at the base of Q1)

Case (1): rin=rpi+beta*2re  (re: diff. resistance of the common emitter path) .

Case (2): rin=2rpi

Case (3): rin=rpi

Case (4): The input resistance at the base of Q1 depends on the signal Vb2 which is applied at the base of Q2. There is no textbook which gives an expression for the input resistance in this case (as far as I know). In this case, the input resistance must be calculated using superposition of the two cases (1) and (3). This is because each arbritrary combination of Vb1 and Vb2 can be split into the cases (1) and (3).

As the result, the formula for the input resistance will contain (and, thus, depend on) both input signals ! Therefore, no compact expression can be given.