For a general constant linear 2nd Order pde, like
DSolve[x''[t] + a x'[t] + b x[t] == 0, x[t], t]
the result gives
{{x[t] ->
E^(1/2 (-a - Sqrt[a^2 - 4 b]) t) C[1] +
E^(1/2 (-a + Sqrt[a^2 - 4 b]) t) C[2]}}
where the repeated root case when b = a^2/4 is ignored, i.e.
DSolve[x''[t] + a x'[t] + b x[t] == 0, x[t], t] /. {b -> a^2/4}
will give
{{x[t] -> E^(-((a t)/2)) (C[1] + t C[2])}}
In general, these two cases are different. So is there a way to use DSolve to give us a conditional expression containing repeated root case?
