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               _
   _       _ _(_)_     |  A fresh approach to technical computing
  (_)     | (_) (_)    |  Documentation: http://docs.julialang.org
   _ _   _| |_  __ _   |  Type "?help" for help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 0.4.6 (2016-06-19 17:16 UTC)
 _/ |\__'_|_|_|\__'_|  |  Official http://julialang.org/ release
|__/                   |  x86_64-w64-mingw32

julia> using ODE

julia> using DifferentialEquations

julia> Pkg.update()
INFO: Updating METADATA...
INFO: Cloning cache of ODE from git://github.com/JuliaLang/ODE.jl.git
INFO: Updating ODE...
INFO: Updating DifferentialEquations...
INFO: Computing changes...
INFO: No packages to install, update or remove

julia> Pkg.rm("ODE")
INFO: No packages to install, update or remove
INFO: Package database updated

julia>

julia> using DifferentialEquations, Plots

julia>

julia> """Example problem with solution ``u(t)=u0*exp(α*t)``"""
"Example problem with solution ``u(t)=u0*exp(α*t)``"

julia> function vanDerPolExample(u0=[0;sqrt(3)])
         f1(u,t) = (1-u[2].^2)*u[1] - u[2]
         f2(u,t) = u[1]
         f(u,t) = [f1(u,t);f2(u,t)]
         return(ODEProblem(f,u0))
       end
vanDerPolExample (generic function with 2 methods)

julia> prob = vanDerPolExample()
DifferentialEquations.ODEProblem(f,[0.0,1.7320508075688772],(anonymous function),false,2,(2,))

julia>

julia> δt = 1//2^(4) #The initial timestepping size. It will automatically assigjulia> δt = 1//2^(4) #The initial timestepping size. It will automatically assigned if not given.
1//16

julia> tspan = [0,20] # The timespan. This is the default if not given.
2-element Array{Int64,1}:
  0
 20

julia>

julia> sol =solve(prob::ODEProblem,tspan,δt=δt,alg=:ode45)
[DifferentialEquations.jl] Initializing backend: ODEJL
DifferentialEquations.ODESolution, 225 timesteps, final value [-0.4319028971751859,1.9224255971025037]