Should it work like this?
using OrdinaryDiffEq
f(u,p,t) = 1.01*u
u0 = 1/2
tspan = (0.0,1.0)
prob = ODEProblem(f,u0,tspan)
sol = solve(prob, Tsit5(), saveat=[0.0,0.0,0.5,0.5,1.0,1.0])
println(sol.t)
[0.0, 0.5, 0.5, 1.0, 1.0] # why no dubbel 0.0 like the others?