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?
