# Plot sol of differentialequation
**URL:** https://discourse.julialang.org/t/plot-sol-of-differentialequation/108768
**Category:** Visualization
**Tags:** plots, differentialequation
**Created:** [January 13, 2024, 12:53pm UTC](https://discourse.julialang.org/t/plot-sol-of-differentialequation/108768 "2024-01-13T12:53:27Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@Stephen](https://discourse.julialang.org/u/Stephen)
#### Post date: [January 13, 2024, 12:53pm UTC](https://discourse.julialang.org/t/plot-sol-of-differentialequation/108768/1 "2024-01-13T12:53:27Z")
```julia
using Plots, DifferentialEquations
function projectile_motion(v₀, θ)
g = 9.8067 # acceleration due to gravity (m/s^2)
t_final = 2 * v₀ * sind(θ) / g # total flight time
# Define the system of second-order ODEs
function projectile!(du, u, p, t)
x, y = u
ddu = [0 -g]
end
# Initial conditions
(u₀, du₀) = [[0.0 0.0], [v₀ * cosd(θ) v₀ * sind(θ)]]
# Time span
t_span = [0.0, 20]
# Solve the ODE
prob = SecondOrderODEProblem(projectile!, du₀, u₀, t_span)
sol = solve(prob, Tsit5(), dt=0.001)
return sol # return the value of du u
end
# Initial velocity and launch angle
v₀ = 100.0 # initial velocity in m/s
θ = 45.0 # launch angle in degrees
# Simulate projectile motion
sol = projectile_motion(v₀, θ)
```
the type of sol.u is a Vector
Plot the results gives：
```julia
plot(sol, title = "Projectile Motion", xaxis = "Time in Seconds",
yaxis = "Velocity (m/s) | Position(m)",labels = ["x Velocity" "y Velocity" "x Position" "y Position"], widen = true, xlims = (0.0, 20.0), ylims = (-500.0, 1500.0))
```
using ` twinx()` how to display velocity and position separately？ what syntax can change the structure or type of sol.u？
by the way, I want labels box off，what syntax should be used？
---
### Author:  [@rafael.guerra](https://discourse.julialang.org/u/rafael.guerra)
#### Post date: [January 13, 2024, 2:32pm UTC](https://discourse.julialang.org/t/plot-sol-of-differentialequation/108768/2 "2024-01-13T14:32:30Z")
Try this [edited code]:
```julia
using Plots, Measures
plot(sol, idxs=1, c=:blue, label=false, xlabel="", ylabel="Velocity [m/s]", margin=10mm)
plot!(sol, idxs=2, c=:blues, label=false, xlabel="", yguidefontcolor=:blue)
p2 = twinx()
plot!(p2, sol, idxs=3, c=:red, label=false, xlabel="", ylabel="Position [m]", yguidefontcolor=:red)
plot!(p2, sol, idxs=4, c=:reds, label=false, xlabel="\nTime [s]")
```
---
### Author:  [@Stephen](https://discourse.julialang.org/u/Stephen)
#### Post date: [January 14, 2024, 1:33am UTC](https://discourse.julialang.org/t/plot-sol-of-differentialequation/108768/3 "2024-01-14T01:33:33Z")
it works ok, yet not perfect, thanks anyway
---
### Author:  [@rafael.guerra](https://discourse.julialang.org/u/rafael.guerra)
#### Post date: [January 14, 2024, 4:58am UTC](https://discourse.julialang.org/t/plot-sol-of-differentialequation/108768/4 "2024-01-14T04:58:34Z")
Please check the revised code above.
It produces this plot:
