Using the IterableTables interface, the DifferentialEquations.jl solutions are presented as tables and directly convert to dataframes:

http://docs.juliadiffeq.org/latest/features/io.html#Tabular-...

f_2dlinear = (du,u,p,t) -> du.=1.01u

prob = ODEProblem(f_2dlinear,rand(2,2),(0.0,1.0))

sol1 =solve(prob,Euler();dt=1//2^(4))

using DataFrames

df = DataFrame(sol1)

# Result 17×5 DataFrames.DataFrame │ Row │ timestamp │ value 1 │ value 2 │ value 3 │ value 4 │ ├─────┼───────────┼──────────┼──────────┼──────────┼──────────┤ │ 1 │ 0.0 │ 0.110435 │ 0.569561 │ 0.918336 │ 0.508044 │ │ 2 │ 0.0625 │ 0.117406 │ 0.605515 │ 0.976306 │ 0.540114 │ ...