In[]:=
DSolve[{d'[t]==C1Exp[-gt]-cd[t],d[0]==D0},d[t],t]
Out[]=
d[t]-C1+cD0+C1-D0g
-ct
(c-g)t
c-g
In[]:=
Simplifyd[t]-C1+cD0+C1-D0g
-ct
(c-g)t
c-g
Out[]=
d[t]C1(-1+)+D0(c-g)
-ct
(c-g)t
c-g
In[]:=
DSolve[{b'[t]==C2/d[t]^n-cb[t],b[0]==B0},b[t],t]
Out[]=
b[t]B0+C2K[1]
-ct
t
∫
0
cK[1]
-n
d[K[1]]