Hello,

I am trying to solve the following system of two coupled differential equations.

sol1 = DSolve[
  {
   a'[t] == - 2 I g (a[t] + Exp[- I 2 g t] * b[t]),
   b'[t] ==   2 I g (b[t] + Exp[  I 2 g t] * a[t]),

   a[0] == 0,
   b[0] == 1
   }, {a, b}, t]

which does not work. And I do not understand why as it has an analytic solution. It is simple to see by substituting a[t],b[t] in the following way:

a[t_] := Exp[-2 I t g]  aa[t]
b[t_] := Exp[ 2 I t g ]  bb[t] 

sol1 = DSolve[
  {
   a'[t] == - 2 I g (a[t] + Exp[- I 2 g t] * b[t]),
   b'[t] ==   2 I g( b[t] + Exp[  I 2 g t] * a[t]),

   a[0]== 0,
   b[0]== 1
}, {aa, bb}, t]

I do not understand, why one version works, while the other does not? Any hints would be appreciated. What did I miss?