DifferentialEquations and derivatives of solutions?

General Usage
3

You just add a second argument with the order of derivative you want:

julia> begin
           using DifferentialEquations
           f(u,p,t) = 1.1*u
           u0 = 1/2
           tspan = (0.0,1.0)
           prob = ODEProblem(f,u0,tspan)
           sol = solve(prob, Tsit5(), reltol=1e-10, abstol=1e-10)
       end;

julia> sol(1.0) # solution at t = 1.0
1.50208301197696

julia> sol(1.0, Val{1}) ) # First derivative of the solution at t = 1.0 
1.6522913131746269

julia> 1.1 * sol(1.0) ≈ sol(1.0, Val{1}) # We know for this differential equation, that this should match the derivative for any t
true
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