We solve the differential equations for a, b, and c as functions of time with the rate constants k1 and k2 in each.

Input := 


sol = DSolve[{eqa,eqb,eqc,a[0]==1,b[0]==0, c[0]==0},

			{a[t],b[t],c[t]},t]

Output =


                1                 k1

{{a[t] -> -------------- - -----------------, 

           k1 t      k1     k1 t      k1

          E     (1 - --)   E     (1 - --) k2

                     k2               k2

                  k1                  k1

   b[t] -> ----------------- - -----------------, 

            k1 t      k1        k2 t      k1

           E     (1 - --) k2   E     (1 - --) k2

                      k2                  k2

                     1                 k1

   c[t] -> 1 - -------------- + -----------------}}

                k1 t      k1     k2 t      k1

               E     (1 - --)   E     (1 - --) k2

                          k2               k2