Undefined constants of ODE solution

Hi,

I have two ODE, one is homogenous and other is nonhomogenous. The similarity of them is the same left hand side (except equ_2 with G while equ_1 without G).

Obviously, they are different equations therefore the undefined constant should be different.

But the solution from dsolve is not such thing. It leads to mistakes when I want to add these two solution. (Just add the two C_1 from two different solution.)

Here is the code.

eqn_1 = -V_T*mu_p*diff(p,x,2) + F*mu_p*diff(p,x) + r_m*p == 0; 
p_dark(x) = dsolve(eqn_1) 

eqn_2 = -V_T*mu_p*diff(p,x,2) + F*mu_p*diff(p,x) + r_m*p -G(x,lumda) == 0; 
p_ph(x,lumda) = dsolve(eqn_2)

So my question is

why the solutions have the same C1 and C2 in two different ODE? What should I do to get a different undefined constant? Like C_1 C_2 for equ_1 and C_3 C_4 for equ_2?

I find this problem in version 2021b. But when I used 2019a, the results are what I want.

Thanks in advance

Jason