# Problem in getting a solution using the package "ReachabilityAnalysis.jl"

**URL:** <https://discourse.julialang.org/t/problem-in-getting-a-solution-using-the-package-reachabilityanalysis-jl/96409>\
**Category:** General Usage\
**Tags:** question\
**Created:** [March 21, 2023, 5:47pm UTC](https://discourse.julialang.org/t/problem-in-getting-a-solution-using-the-package-reachabilityanalysis-jl/96409 "2023-03-21T17:47:57Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![Ashu](https://avatars.discourse-cdn.com/v4/letter/a/4bbf92/32.png) [@Ashu](https://discourse.julialang.org/u/Ashu)\
**Post date:** [March 21, 2023, 5:47pm UTC](https://discourse.julialang.org/t/problem-in-getting-a-solution-using-the-package-reachabilityanalysis-jl/96409/1 "2023-03-21T17:47:57Z")

</div>

Hello all,

I am trying to solve a differential equation with interval coefficients using the packages “IntervalArithmetic.jl” and “ReachabilityAnalysis.jl” in Pluto.jl notebook. When I tried to plot the solution I got this plot  
 ![Julia_plot](https://global.discourse-cdn.com/julialang/original/3X/3/2/3256e7aa4b08d9c7d271dd0c7e62841c1bf0e6ad.png)

I wish to get a complete blue color plot (10 seconds), but I am getting it for less than 2 seconds. Could you please let me know what is the problem and how can I resolve it?  
I used the code shown below-

```julia
begin	
	@taylorize function f(du, u, p, t)
		du[1] = ( u[1] + u[2] ) * ( u[1] - u[3] ) * ( u[1] + u[4] )

		#encode uncertain params
		du[2] = zero(u[1]) # p[1]
		du[3] = zero(u[1]) # p[2]
		du[4] = zero(u[1]) # p[3]
	end

	p_int = (1.0..1.0) × (2.0..2.01) × (3.0..3.0)
	U0 = Singleton([1.0]) × convert(Hyperrectangle, p_int)
	prob = @ivp(u' = f(u), dim: 4, u(0) ∈ U0);
	sol = solve(prob, tspan=(0.0, 10.0), TMJets(abstol=1e-5));
	solz = overapproximate(sol, Zonotope);

	function g(du, u, p, t)
		a, b, c = p
		n = 1
		du[1] = ( u[1] + a ) * ( u[1] - b ) * ( u[1] + c)
	end
	
	u0 = [1.0] # initial conditions
	p = (1.0, 2.0, 3.0) # unperturbed parameter values
	tspan = (0.0, 10.0) # time span to solve the system over
	prob = ODEProblem(g, u0, tspan, p)
	sol = solve(prob)
	
	#plot
	plot(solz, vars=(0, 1), lw=0.3)
	plot!(sol, vars=(0, 1), legend=false, ylabel="x(t)", xlabel="Time")
	savefig("Julia_plot.png")
end

```