# How to plot square root of solution to an ODE

**URL:** <https://discourse.julialang.org/t/how-to-plot-square-root-of-solution-to-an-ode/39272>\
**Category:** New to Julia\
**Created:** [May 11, 2020, 10:16am UTC](https://discourse.julialang.org/t/how-to-plot-square-root-of-solution-to-an-ode/39272 "2020-05-11T10:16:57Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![Manoj\_Gopalkrishnan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/manoj_gopalkrishnan/32/14587_2.png) [@Manoj\_Gopalkrishnan](https://discourse.julialang.org/u/Manoj_Gopalkrishnan)\
**Post date:** [May 11, 2020, 10:16am UTC](https://discourse.julialang.org/t/how-to-plot-square-root-of-solution-to-an-ode/39272/1 "2020-05-11T10:16:57Z")

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Hi,

I have an ODEProblem, let us say like the one in this example: [https://docs.sciml.ai/stable/tutorials/ode\_example/](https://docs.sciml.ai/stable/tutorials/ode_example/)

```julia
function parameterized_lorenz!(du,u,p,t)
 du[1] = p[1]*(u[2]-u[1])
 du[2] = u[1]*(p[2]-u[3]) - u[2]
 du[3] = u[1]*u[2] - p[3]*u[3]
end

u0 = [1.0,0.0,0.0]
tspan = (0.0,1.0)
p = [10.0,28.0,8/3]
prob = ODEProblem(parameterized_lorenz!,u0,tspan,p)

```

I solve this ODE using solve() and want to plot time versus square root of the second coordinate. How can I do this?

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<div class="post-metadata">

**Author:** ![Manoj\_Gopalkrishnan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/manoj_gopalkrishnan/32/14587_2.png) [@Manoj\_Gopalkrishnan](https://discourse.julialang.org/u/Manoj_Gopalkrishnan)\
**Post date:** [May 11, 2020, 11:02am UTC](https://discourse.julialang.org/t/how-to-plot-square-root-of-solution-to-an-ode/39272/2 "2020-05-11T11:02:03Z")

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I managed to do this, but feels like a hack:

```julia
plot(1:29,sqrt.(Array(sol)'[:,2]))

```

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<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [May 11, 2020, 11:55am UTC](https://discourse.julialang.org/t/how-to-plot-square-root-of-solution-to-an-ode/39272/3 "2020-05-11T11:55:45Z")

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It’s mentioned in the plotting page: [https://docs.sciml.ai/latest/basics/plot/](https://docs.sciml.ai/latest/basics/plot/)

```julia
plot(sol,vars=(sqrt,0,2))

```

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<div class="post-metadata">

**Author:** ![Manoj\_Gopalkrishnan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/manoj_gopalkrishnan/32/14587_2.png) [@Manoj\_Gopalkrishnan](https://discourse.julialang.org/u/Manoj_Gopalkrishnan)\
**Post date:** [May 11, 2020, 12:22pm UTC](https://discourse.julialang.org/t/how-to-plot-square-root-of-solution-to-an-ode/39272/4 "2020-05-11T12:22:40Z")

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Thanks! That almost worked, I had to make a small change:

```julia
f(x,y) = return (x,sqrt(y))
plot(sol,vars=(f,0,2))

```

since the compiler is expecting f to be a function of two variables here.