# Solving ODE with vector Argument

Dear Friends

I am trying to solve an ode problem function myfun(du,u,p,t)

where u consists of the vectors x,z,e. I want this function return solution just for e
(I do not know how must I do this)

Here is the code which I have used for it

using DifferentialEquations
using LinearAlgebra
using Plots
function myfun(du,u,p,t)
x, z, e = u
du[1] = dx[1] = x[2]
du[2] = dx[2] = -p[1]^2*((1-cos(x[1]))^2/sin(x[1])^3)-p[2]*sin(x[1])-p[3]*x[2]-p[4]*x[2]^3+(p[2]+p[6]*sin(p[5]*t))sin(x[1])
du[3]=dz[1]=z[2]
du[4]=dz[2]=-p[1]^2
((1-cos(z[1]))^2/sin(z[1])^3)-p[2]*sin(z[1])-p[3]*z[2]-p[4]z[2]^3+(p[2]+p[6]sin(p[5]t))sin(z[1])+0.000001sin(x[1])+0.4sin(pit)
du[5]=de[1]=x[2]-z[2]
du[6]=de[2]=-p[1]^2
((1-cos(x[1]))^2/sin(x[1])^3)-p[2]*sin(x[1])-p[3]*x[2]-p[4]*x[2]^3+(p[2]+p[6]*sin(p[5]*t))sin(x[1])-(-p[1]^2((1-cos(z[1]))^2/sin(z[1])^3)-p[2]*sin(z[1])-p[3]*z[2]-p[4]*z[2]^3+(p[2]+p[6]sin(p[5]t))sin(z[1])+0.000001sin(x[1])+0.4sin(pit))
end
u0 = [1;-1;1.6;0.8;0;-1.8]
tspan = (0.0,10.0)
p = [1.5,1.0,3.0,1.0]
prob = ODEProblem(myfun,u0,tspan,p)
sol=solve(prob)

ERROR: BoundsError
Stacktrace:
[1] getindex
@ .\number.jl:96 [inlined]
[2] myfun(du::Vector{Float64}, u::Vector{Float64}, p::Vector{Float64}, t::Float64)
@ Main .\REPL[4]:3
[3] ODEFunction
@ C:\Users\user.julia\packages\SciMLBase\oTP8b\src\scimlfunctions.jl:334 [inlined]
[4] initialize!(integrator::OrdinaryDiffEq.ODEIntegrator{CompositeAlgorithm{Tuple{Tsit5, Rosenbrock23{0, false, DefaultLinSolve, DataType}}, OrdinaryDiffEq.AutoSwitchCache{Tsit5, Rosenbrock23{0, false, DefaultLinSolve, DataType}, Rational{Int64}, Int64}}, true, Vector{Float64}, Nothing, Float64, Vector{Float64}, Float64, Float64, Float64, Float64, Vector{Vector{Float64}}, OrdinaryDiffEq.ODECompositeSolution{Float64, 2, Vector{Vector{Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Vector{Float64}, ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, CompositeAlgorithm{Tuple{Tsit5, Rosenbrock23{0, false, DefaultLinSolve, DataType}}, OrdinaryDiffEq.AutoSwitchCache{Tsit5, Rosenbrock23{0, false, DefaultLinSolve, DataType}, Rational{Int64}, Int64}}, OrdinaryDiffEq.CompositeInterpolationData{ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}}, OrdinaryDiffEq.Rosenbrock23Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, Matrix{Float64}, Matrix{Float64}, OrdinaryDiffEq.Rosenbrock23Tableau{Float64}, SciMLBase.TimeGradientWrapper{ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Vector{Float64}, Vector{Float64}}, SciMLBase.UJacobianWrapper{ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Float64, Vector{Float64}}, DefaultLinSolve, FiniteDiff.JacobianCache{Vector{Float64}, Vector{Float64}, Vector{Float64}, UnitRange{Int64}, Nothing, Val{:forward}(), Float64}, FiniteDiff.GradientCache{Nothing, Vector{Float64}, Vector{Float64}, Float64, Val{:forward}(), Float64, Val{true}()}}}, OrdinaryDiffEq.AutoSwitchCache{Tsit5, Rosenbrock23{0, false, DefaultLinSolve, DataType}, Rational{Int64}, Int64}}}, DiffEqBase.DEStats}, ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}}, OrdinaryDiffEq.Rosenbrock23Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, Matrix{Float64}, Matrix{Float64}, OrdinaryDiffEq.Rosenbrock23Tableau{Float64}, SciMLBase.TimeGradientWrapper{ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Vector{Float64}, Vector{Float64}}, SciMLBase.UJacobianWrapper{ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Float64, Vector{Float64}}, DefaultLinSolve, FiniteDiff.JacobianCache{Vector{Float64}, Vector{Float64}, Vector{Float64}, UnitRange{Int64}, Nothing, Val{:forward}(), Float64}, FiniteDiff.GradientCache{Nothing, Vector{Float64}, Vector{Float64}, Float64, Val{:forward}(), Float64, Val{true}()}}}, OrdinaryDiffEq.AutoSwitchCache{Tsit5, Rosenbrock23{0, false, DefaultLinSolve, DataType}, Rational{Int64}, Int64}}, OrdinaryDiffEq.DEOptions{Float64, Float64, Float64, Float64, PIController{Rational{Int64}}, typeof(DiffEqBase.ODE_DEFAULT_NORM), typeof(opnorm), Nothing, CallbackSet{Tuple{}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), DataStructures.BinaryMinHeap{Float64}, DataStructures.BinaryMinHeap{Float64}, Nothing, Nothing, Int64, Tuple{}, Tuple{}, Tuple{}}, Vector{Float64}, Float64, Nothing, OrdinaryDiffEq.DefaultInit}, cache::OrdinaryDiffEq.Tsit5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}})
@ OrdinaryDiffEq C:\Users\user.julia\packages\OrdinaryDiffEq\a5qvy\src\perform_step\low_order_rk_perform_step.jl:623
[5] initialize!(integrator::OrdinaryDiffEq.ODEIntegrator{CompositeAlgorithm{Tuple{Tsit5, Rosenbrock23{0, false, DefaultLinSolve, DataType}}, OrdinaryDiffEq.AutoSwitchCache{Tsit5, Rosenbrock23{0, false, DefaultLinSolve, DataType}, Rational{Int64}, Int64}}, true, Vector{Float64}, Nothing, Float64, Vector{Float64}, Float64, Float64, Float64, Float64, Vector{Vector{Float64}}, OrdinaryDiffEq.ODECompositeSolution{Float64, 2, Vector{Vector{Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Vector{Float64}, ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, CompositeAlgorithm{Tuple{Tsit5, Rosenbrock23{0, false, DefaultLinSolve, DataType}}, OrdinaryDiffEq.AutoSwitchCache{Tsit5, Rosenbrock23{0, false, DefaultLinSolve, DataType}, Rational{Int64}, Int64}}, OrdinaryDiffEq.CompositeInterpolationData{ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}}, OrdinaryDiffEq.Rosenbrock23Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, Matrix{Float64}, Matrix{Float64}, OrdinaryDiffEq.Rosenbrock23Tableau{Float64}, SciMLBase.TimeGradientWrapper{ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Vector{Float64}, Vector{Float64}}, SciMLBase.UJacobianWrapper{ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Float64, Vector{Float64}}, DefaultLinSolve, FiniteDiff.JacobianCache{Vector{Float64}, Vector{Float64}, Vector{Float64}, UnitRange{Int64}, Nothing, Val{:forward}(), Float64}, FiniteDiff.GradientCache{Nothing, Vector{Float64}, Vector{Float64}, Float64, Val{:forward}(), Float64, Val{true}()}}}, OrdinaryDiffEq.AutoSwitchCache{Tsit5, Rosenbrock23{0, false, DefaultLinSolve, DataType}, Rational{Int64}, Int64}}}, DiffEqBase.DEStats}, ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}}, OrdinaryDiffEq.Rosenbrock23Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, Matrix{Float64}, Matrix{Float64}, OrdinaryDiffEq.Rosenbrock23Tableau{Float64}, SciMLBase.TimeGradientWrapper{ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Vector{Float64}, Vector{Float64}}, SciMLBase.UJacobianWrapper{ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Float64, Vector{Float64}}, DefaultLinSolve, FiniteDiff.JacobianCache{Vector{Float64}, Vector{Float64}, Vector{Float64}, UnitRange{Int64}, Nothing, Val{:forward}(), Float64}, FiniteDiff.GradientCache{Nothing, Vector{Float64}, Vector{Float64}, Float64, Val{:forward}(), Float64, Val{true}()}}}, OrdinaryDiffEq.AutoSwitchCache{Tsit5, Rosenbrock23{0, false, DefaultLinSolve, DataType}, Rational{Int64}, Int64}}, OrdinaryDiffEq.DEOptions{Float64, Float64, Float64, Float64, PIController{Rational{Int64}}, typeof(DiffEqBase.ODE_DEFAULT_NORM), typeof(opnorm), Nothing, CallbackSet{Tuple{}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), DataStructures.BinaryMinHeap{Float64}, DataStructures.BinaryMinHeap{Float64}, Nothing, Nothing, Int64, Tuple{}, Tuple{}, Tuple{}}, Vector{Float64}, Float64, Nothing, OrdinaryDiffEq.DefaultInit}, cache::OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}}, OrdinaryDiffEq.Rosenbrock23Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, Matrix{Float64}, Matrix{Float64}, OrdinaryDiffEq.Rosenbrock23Tableau{Float64}, SciMLBase.TimeGradientWrapper{ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Vector{Float64}, Vector{Float64}}, SciMLBase.UJacobianWrapper{ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Float64, Vector{Float64}}, DefaultLinSolve, FiniteDiff.JacobianCache{Vector{Float64}, Vector{Float64}, Vector{Float64}, UnitRange{Int64}, Nothing, Val{:forward}(), Float64}, FiniteDiff.GradientCache{Nothing, Vector{Float64}, Vector{Float64}, Float64, Val{:forward}(), Float64, Val{true}()}}}, OrdinaryDiffEq.AutoSwitchCache{Tsit5, Rosenbrock23{0, false, DefaultLinSolve, DataType}, Rational{Int64}, Int64}})
@ OrdinaryDiffEq C:\Users\user.julia\packages\OrdinaryDiffEq\a5qvy\src\perform_step\composite_perform_step.jl:39
[6] __init(prob::ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Vector{Float64}, ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, alg::CompositeAlgorithm{Tuple{Tsit5, Rosenbrock23{0, false, DefaultLinSolve, DataType}}, AutoSwitch{Tsit5, Rosenbrock23{0, false, DefaultLinSolve, DataType}, Rational{Int64}, Int64}}, timeseries_init::Tuple{}, ts_init::Tuple{}, ks_init::Tuple{}, recompile::Type{Val{true}}; saveat::Tuple{}, tstops::Tuple{}, d_discontinuities::Tuple{}, save_idxs::Nothing, save_everystep::Bool, save_on::Bool, save_start::Bool, save_end::Nothing, callback::Nothing, dense::Bool, calck::Bool, dt::Float64, dtmin::Nothing, dtmax::Float64, force_dtmin::Bool, adaptive::Bool, gamma::Rational{Int64}, abstol::Nothing, reltol::Nothing, qmin::Rational{Int64}, qmax::Int64, qsteady_min::Int64, qsteady_max::Int64, beta1::Nothing, beta2::Nothing, qoldinit::Rational{Int64}, controller::Nothing, fullnormalize::Bool, failfactor::Int64, maxiters::Int64, internalnorm::typeof(DiffEqBase.ODE_DEFAULT_NORM), internalopnorm::typeof(opnorm), isoutofdomain::typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), unstable_check::typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), verbose::Bool, timeseries_errors::Bool, dense_errors::Bool, advance_to_tstop::Bool, stop_at_next_tstop::Bool, initialize_save::Bool, progress::Bool, progress_steps::Int64, progress_name::String, progress_message::typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), userdata::Nothing, allow_extrapolation::Bool, initialize_integrator::Bool, alias_u0::Bool, alias_du0::Bool, initializealg::OrdinaryDiffEq.DefaultInit, kwargs::Base.Iterators.Pairs{Symbol, Bool, Tuple{Symbol, Symbol}, NamedTuple{(:default_set, :second_time), Tuple{Bool, Bool}}})
@ OrdinaryDiffEq C:\Users\user.julia\packages\OrdinaryDiffEq\a5qvy\src\solve.jl:456
[7] __solve(::ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Vector{Float64}, ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, ::CompositeAlgorithm{Tuple{Tsit5, Rosenbrock23{0, false, DefaultLinSolve, DataType}}, AutoSwitch{Tsit5, Rosenbrock23{0, false, DefaultLinSolve, DataType}, Rational{Int64}, Int64}}; kwargs::Base.Iterators.Pairs{Symbol, Bool, Tuple{Symbol, Symbol}, NamedTuple{(:default_set, :second_time), Tuple{Bool, Bool}}})
@ OrdinaryDiffEq C:\Users\user.julia\packages\OrdinaryDiffEq\a5qvy\src\solve.jl:4
[8] __solve(::ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Vector{Float64}, ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, ::Nothing; default_set::Bool, kwargs::Base.Iterators.Pairs{Symbol, Bool, Tuple{Symbol}, NamedTuple{(:second_time,), Tuple{Bool}}})
@ DifferentialEquations C:\Users\user.julia\packages\DifferentialEquations\ddA0E\src\default_solve.jl:7
[9] #__solve#73
@ C:\Users\user.julia\packages\DiffEqBase\oe7VF\src\solve.jl:282 [inlined]
[10] __solve
@ C:\Users\user.julia\packages\DiffEqBase\oe7VF\src\solve.jl:269 [inlined]
[11] #solve_call#58
@ C:\Users\user.julia\packages\DiffEqBase\oe7VF\src\solve.jl:61 [inlined]
[12] solve_call
@ C:\Users\user.julia\packages\DiffEqBase\oe7VF\src\solve.jl:48 [inlined]
[13] #solve_up#60
@ C:\Users\user.julia\packages\DiffEqBase\oe7VF\src\solve.jl:85 [inlined]
[14] solve_up
@ C:\Users\user.julia\packages\DiffEqBase\oe7VF\src\solve.jl:75 [inlined]
[15] #solve#59
@ C:\Users\user.julia\packages\DiffEqBase\oe7VF\src\solve.jl:70 [inlined]
[16] solve(::ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Vector{Float64}, ODEFunction{true, typeof(myfun), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem})
@ DiffEqBase C:\Users\user.julia\packages\DiffEqBase\oe7VF\src\solve.jl:68
[17] top-level scope
@ REPL[9]:1

I do not know if I have act in a right way

and How must I solve this and then pick up e.